# Reports and developer tools

Choose a defined job, inspect its input and result example, then review the available payment options. Each is a one-time job with private result access for 30 days. Save a downloaded copy.

## Kelvin Bipolar Resistance Record

Service ID: `kelvin-bipolar-resistance-record`. USD 9.00 per job.

Separate resistance and constant thermoelectric offset from opposite-current four-terminal voltage observations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /resistanceOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=kelvin-bipolar-resistance-record) · [Technical reference](https://www.tek.com/en/documents/technical-article/low-voltage-measurement-techniques)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "plusV": 3,
      "minusV": -1,
      "currentA": 2,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/resistanceOhm": 1,
  "/records/0/thermalOffsetV": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/resistanceOhm",
  "/records/0/comparisonAvailable": true
}
```

## Delta Reversal Resistance Record

Service ID: `delta-reversal-resistance-record`. USD 9.00 per job.

Resolve three equally spaced plus-minus-plus readings into drift-cancelled resistance and observed voltage drift. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /resistanceOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=delta-reversal-resistance-record) · [Technical reference](https://www.tek.com/en/documents/technical-article/low-voltage-measurement-techniques)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "v1": 3,
      "v2": -1,
      "v3": 5,
      "currentA": 2,
      "reportedValue": 1.25,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/resistanceOhm": 1.25,
  "/records/0/driftVPerInterval": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/resistanceOhm",
  "/records/0/comparisonAvailable": true
}
```

## Voltmeter Loading Source Record

Service ID: `voltmeter-loading-source-record`. USD 9.00 per job.

Reconstruct a Thevenin source voltage and the recorded loading bias from a finite-resistance voltmeter. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /unloadedV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=voltmeter-loading-source-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "indicationV": 4,
      "meterOhm": 4,
      "sourceOhm": 1,
      "reportedValue": 5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/unloadedV": 5,
  "/records/0/loadingBiasV": -1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/unloadedV",
  "/records/0/comparisonAvailable": true
}
```

## Ammeter Burden Branch Record

Service ID: `ammeter-burden-branch-record`. USD 9.00 per job.

Separate ammeter burden and intended branch resistance using simultaneous source, current and burden observations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /loadOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ammeter-burden-branch-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sourceV": 12,
      "currentA": 2,
      "burdenV": 2,
      "reportedValue": 5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/loadOhm": 5,
  "/records/0/burdenOhm": 1,
  "/records/0/loadPowerW": 20,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/loadOhm",
  "/records/0/comparisonAvailable": true
}
```

## Passive Probe Compensation Record

Service ID: `passive-probe-compensation-record`. USD 9.00 per job.

Compare the high- and low-frequency attenuation of a passive compensated divider with supplied parasitic capacitances. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /dcRatio using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=passive-probe-compensation-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "probeOhm": 9,
      "inputOhm": 1,
      "probeF": 1,
      "inputF": 9,
      "reportedValue": 0.1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/dcRatio": 0.1,
  "/records/0/fastRatio": 0.1,
  "/records/0/timeConstantMismatchS": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/dcRatio",
  "/records/0/comparisonAvailable": true
}
```

## Scope Step Rise Time Deembedding Record

Service ID: `scope-step-rise-time-deembedding-record`. USD 9.00 per job.

Extract 10-to-90-percent rise time from a supplied monotone finite step trace, then deembed a declared Gaussian instrument rise time and reconcile the device bandwidth proxy. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /observedRiseS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=scope-step-rise-time-deembedding-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2,
        3,
        4
      ],
      "volts": [
        0,
        0.1,
        0.5,
        0.9,
        1
      ],
      "baselineV": 0,
      "plateauV": 1,
      "instrumentS": 1.2,
      "bandwidthRiseProduct": 0.35,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/observedRiseS": 2,
  "/records/0/deviceRiseS": 1.6,
  "/records/0/deviceBandwidthHz": 0.21875,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/observedRiseS",
  "/records/0/comparisonAvailable": true
}
```

## Shunt Self Heating Operating Point Record

Service ID: `shunt-self-heating-operating-point-record`. USD 9.00 per job.

Solve constant-current shunt self-heating with linear temperature coefficient and lumped thermal resistance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /hotOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=shunt-self-heating-operating-point-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "currentA": 2,
      "coldOhm": 1,
      "tempCoefficient": 0.01,
      "thermalKPerW": 1,
      "reportedValue": 1.0416666666666667,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/hotOhm": 1.0416666666666667,
  "/records/0/powerW": 4.166666666666667,
  "/records/0/riseK": 4.166666666666667,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/hotOhm",
  "/records/0/comparisonAvailable": true
}
```

## Two Temperature Resistance Coefficient Record

Service ID: `two-temperature-resistance-coefficient-record`. USD 9.00 per job.

Fit reference resistance and linear TCR from two resistance-temperature observations around an explicit reference. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /referenceOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-temperature-resistance-coefficient-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "t1C": 0,
      "t2C": 10,
      "r1Ohm": 10,
      "r2Ohm": 11,
      "referenceC": 0,
      "reportedValue": 10,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/referenceOhm": 10,
  "/records/0/coefficientPerK": 0.01,
  "/records/0/slopeOhmPerK": 0.1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/referenceOhm",
  "/records/0/comparisonAvailable": true
}
```

## Divider Tolerance Envelope Record

Service ID: `divider-tolerance-envelope-record`. USD 9.00 per job.

Reconcile nominal and independent worst-case divider fractions with declared resistor tolerance bounds. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /nominal using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=divider-tolerance-envelope-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "topOhm": 3,
      "bottomOhm": 1,
      "topFraction": 0.1,
      "bottomFraction": 0.1,
      "reportedValue": 0.25,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/nominal": 0.25,
  "/records/0/minimum": 0.21428571428571427,
  "/records/0/maximum": 0.2894736842105263,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/nominal",
  "/records/0/comparisonAvailable": true
}
```

## Full Wheatstone Excitation Record

Service ID: `full-wheatstone-excitation-record`. USD 9.00 per job.

Reconcile nonlinear four-arm bridge differential voltage and common-mode level with explicit source excitation. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /differentialV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=full-wheatstone-excitation-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "r1": 1,
      "r2": 1,
      "r3": 1,
      "r4": 3,
      "excitationV": 8,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/differentialV": 2,
  "/records/0/commonModeV": 5,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/differentialV",
  "/records/0/comparisonAvailable": true
}
```

## Potentiometer Drift Bracket Record

Service ID: `potentiometer-drift-bracket-record`. USD 9.00 per job.

Reconcile a null-comparison unknown voltage against linearly interpolated bracketing reference observations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /unknownV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=potentiometer-drift-bracket-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceV": 10,
      "beforeRatio": 0.9,
      "afterRatio": 1.1,
      "elapsedFraction": 0.5,
      "unknownRatio": 0.5,
      "reportedValue": 5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/unknownV": 5,
  "/records/0/interpolatedReferenceRatio": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/unknownV",
  "/records/0/comparisonAvailable": true
}
```

## Guarded Insulation Current Record

Service ID: `guarded-insulation-current-record`. USD 9.00 per job.

Separate guarded specimen current from guard and blank currents while retaining signed current evidence. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /specimenA using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=guarded-insulation-current-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "appliedV": 100,
      "totalA": 5,
      "guardA": 2,
      "blankA": 1,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/specimenA": 2,
  "/records/0/resistanceOhm": 50,
  "/records/0/guardFraction": 0.5,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/specimenA",
  "/records/0/comparisonAvailable": true
}
```

## Constant Current Capacitance Leakage Record

Service ID: `constant-current-capacitance-leakage-record`. USD 9.00 per job.

Resolve capacitance and parallel leakage from two charging slopes at distinct capacitor voltages. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /capacitanceF using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=constant-current-capacitance-leakage-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "currentA": 3,
      "v1": 1,
      "v2": 2,
      "slope1VPerS": 2,
      "slope2VPerS": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/capacitanceF": 1,
  "/records/0/leakageOhm": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/capacitanceF",
  "/records/0/comparisonAvailable": true
}
```

## Capacitor Absorption Recovery Energy Record

Service ID: `capacitor-absorption-recovery-energy-record`. USD 9.00 per job.

Reconcile recovered voltage fraction and electrostatic recovery energy after a declared discharge/recovery observation. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /absorptionFraction using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=capacitor-absorption-recovery-energy-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "capacitanceF": 2,
      "chargeV": 10,
      "residualV": 1,
      "recoveredV": 3,
      "reportedValue": 0.2222222222222222,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/absorptionFraction": 0.2222222222222222,
  "/records/0/recoveredJ": 8,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/absorptionFraction",
  "/records/0/comparisonAvailable": true
}
```

## Capacitor Dissipation Series Record

Service ID: `capacitor-dissipation-series-record`. USD 9.00 per job.

Reconcile series capacitance loss from a measured dissipation factor and sinusoidal RMS terminal voltage. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /esrOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=capacitor-dissipation-series-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "capacitanceF": 1,
      "omegaRadPerS": 2,
      "tanDelta": 0.1,
      "rmsV": 5,
      "reportedValue": 0.05,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/esrOhm": 0.05,
  "/records/0/currentA": 9.950371902099892,
  "/records/0/lossW": 4.950495049504951,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/esrOhm",
  "/records/0/comparisonAvailable": true
}
```

## Lcr Parallel Equivalent Observation Record

Service ID: `lcr-parallel-equivalent-observation-record`. USD 9.00 per job.

Translate measured parallel conductance and susceptance to a nondegenerate series-equivalent resistance/reactance record. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /seriesR using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lcr-parallel-equivalent-observation-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "conductanceS": 3,
      "susceptanceS": 4,
      "reportedValue": 0.12,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/seriesR": 0.12,
  "/records/0/seriesX": -0.16,
  "/records/0/impedanceOhm": 0.2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/seriesR",
  "/records/0/comparisonAvailable": true
}
```

## Inductor Q Loss Separation Record

Service ID: `inductor-q-loss-separation-record`. USD 9.00 per job.

Separate inductive reactance, series resistance and real sinusoidal loss from LCR magnitude/Q observations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /seriesOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=inductor-q-loss-separation-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "magnitudeOhm": 5,
      "quality": 0.75,
      "omegaRadPerS": 3,
      "rmsA": 2,
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/seriesOhm": 4,
  "/records/0/inductanceH": 1,
  "/records/0/lossW": 16,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/seriesOhm",
  "/records/0/comparisonAvailable": true
}
```

## Transformer Polarity Voltage Closure Record

Service ID: `transformer-polarity-voltage-closure-record`. USD 9.00 per job.

Reconcile isolated winding voltages with measured series-aiding and series-opposing observations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /turnsRatio using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=transformer-polarity-voltage-closure-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "primaryV": 10,
      "secondaryV": 2,
      "aidingV": 12,
      "opposingV": 8,
      "reportedValue": 5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/turnsRatio": 5,
  "/records/0/aidingResidualV": 0,
  "/records/0/opposingResidualV": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/turnsRatio",
  "/records/0/comparisonAvailable": true
}
```

## Ct Complex Ratio Error Record

Service ID: `ct-complex-ratio-error-record`. USD 9.00 per job.

Compare a current-transformer secondary complex observation with its explicitly signed ideal ratio and retain phase displacement. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /ratioErrorFraction using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ct-complex-ratio-error-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "primaryReA": 10,
      "primaryImA": 0,
      "secondaryReA": 2,
      "secondaryImA": 0,
      "ratio": 5,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/ratioErrorFraction": 0,
  "/records/0/phaseErrorRad": 0,
  "/records/0/secondaryErrorA": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/ratioErrorFraction",
  "/records/0/comparisonAvailable": true
}
```

## Instrument Transformer Burden Record

Service ID: `instrument-transformer-burden-record`. USD 9.00 per job.

Reconcile apparent, active and reactive burden from RMS terminal measurements without inferring transformer accuracy. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /apparentVA using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=instrument-transformer-burden-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "voltageV": 10,
      "currentA": 2,
      "watts": 12,
      "reportedValue": 20,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/apparentVA": 20,
  "/records/0/reactiveVar": 16,
  "/records/0/resistanceOhm": 3,
  "/records/0/reactanceMagnitudeOhm": 4,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/apparentVA",
  "/records/0/comparisonAvailable": true
}
```

## Two Wattmeter Balanced Power Record

Service ID: `two-wattmeter-balanced-power-record`. USD 9.00 per job.

Reconcile balanced three-wire two-wattmeter readings into active/reactive power and displacement factor with explicit sign convention. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /activeW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-wattmeter-balanced-power-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "w1": 8,
      "w2": 2,
      "reportedValue": 10,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/activeW": 10,
  "/records/0/reactiveVar": 10.392304845413264,
  "/records/0/powerFactor": 0.6933752452815365,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/activeW",
  "/records/0/comparisonAvailable": true
}
```

## Phase Power Meter Closure Record

Service ID: `phase-power-meter-closure-record`. USD 9.00 per job.

Reconcile independently measured per-phase active powers and their recorded aggregate while retaining each phase sign. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /phaseW/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=phase-power-meter-closure-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "volts": [
        10,
        10,
        10
      ],
      "amps": [
        2,
        2,
        2
      ],
      "cosPhi": [
        1,
        0.5,
        -0.5
      ],
      "aggregateW": 20,
      "reportedValue": 20,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/phaseW": [
    20,
    10,
    -10
  ],
  "/records/0/sumW": 20,
  "/records/0/aggregateResidualW": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/phaseW/0",
  "/records/0/comparisonAvailable": true
}
```

## Delta Voltage Phasor Closure Record

Service ID: `delta-voltage-phasor-closure-record`. USD 9.00 per job.

Review closure of three measured oriented line-to-line voltage phasors and retain the normalized closure residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /closureRealV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=delta-voltage-phasor-closure-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "realV": [
        1,
        -0.5,
        -0.5
      ],
      "imagV": [
        0,
        1,
        -1
      ],
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/closureRealV": 0,
  "/records/0/closureImagV": 0,
  "/records/0/closureMagnitudeV": 0,
  "/records/0/relativeClosure": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/closureRealV",
  "/records/0/comparisonAvailable": true
}
```

## Unbalanced Capacitor Bank Kvar Record

Service ID: `unbalanced-capacitor-bank-kvar-record`. USD 9.00 per job.

Reconcile per-phase reactive power and current of a supplied three-branch ideal capacitor bank at measured branch RMS voltages. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /branchVar/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=unbalanced-capacitor-bank-kvar-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "branchV": [
        2,
        3,
        4
      ],
      "branchF": [
        1,
        1,
        1
      ],
      "omegaRadPerS": 2,
      "reportedValue": 8,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/branchVar": [
    8,
    18,
    32
  ],
  "/records/0/totalVar": 58,
  "/records/0/branchA": [
    4,
    6,
    8
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/branchVar/0",
  "/records/0/comparisonAvailable": true
}
```

## Harmonic Distortion Power Factor Record

Service ID: `harmonic-distortion-power-factor-record`. USD 9.00 per job.

Reconcile orthogonal current harmonic RMS components with sinusoidal voltage displacement factor and total true factor. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /totalRmsA using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=harmonic-distortion-power-factor-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "currentHarmonicA": [
        3,
        4
      ],
      "fundamentalCosPhi": 0.8,
      "reportedValue": 5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/totalRmsA": 5,
  "/records/0/thd": 1.3333333333333333,
  "/records/0/distortionFactor": 0.6,
  "/records/0/truePowerFactor": 0.48,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/totalRmsA",
  "/records/0/comparisonAvailable": true
}
```

## Harmonic Budeanu Power Ledger Record

Service ID: `harmonic-budeanu-power-ledger-record`. USD 9.00 per job.

Reconcile aligned RMS harmonic voltage/current/phase observations into Budeanu active, reactive and distortion-power evidence. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /activeW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=harmonic-budeanu-power-ledger-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "v": [
        3,
        4
      ],
      "i": [
        1,
        2
      ],
      "phaseRad": [
        0,
        0
      ],
      "reportedValue": 11,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/activeW": 11,
  "/records/0/reactiveVar": 0,
  "/records/0/apparentVA": 11.180339887498949,
  "/records/0/distortionVA": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/activeW",
  "/records/0/comparisonAvailable": true
}
```

## Zero Crossing Period Jitter Record

Service ID: `zero-crossing-period-jitter-record`. USD 9.00 per job.

Reconcile strictly ordered same-direction waveform crossings into mean period and cycle-to-cycle jitter. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /meanPeriodS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=zero-crossing-period-jitter-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "crossingS": [
        0,
        1,
        2,
        3
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/meanPeriodS": 1,
  "/records/0/frequencyHz": 1,
  "/records/0/peakToPeakJitterS": 0,
  "/records/0/successiveJitterRmsS": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/meanPeriodS",
  "/records/0/comparisonAvailable": true
}
```

## Adc Code Density Linearity Record

Service ID: `adc-code-density-linearity-record`. USD 9.00 per job.

Reconcile an already uniform-stimulus ADC interior code histogram into DNL and cumulative INL while retaining missing codes. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /dnl/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=adc-code-density-linearity-record) · [Technical reference](https://www.analog.com/en/resources/technical-articles/histogram-testing-determines-dnl-and-inl-errors.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "counts": [
        2,
        4,
        2
      ],
      "reportedValue": -0.25,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/dnl": [
    -0.25,
    0.5,
    -0.25
  ],
  "/records/0/inl": [
    -0.25,
    0.25,
    0
  ],
  "/records/0/missingCodes": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/dnl/0",
  "/records/0/comparisonAvailable": true
}
```

## Adc Missing Code Run Record

Service ID: `adc-missing-code-run-record`. USD 9.00 per job.

Locate contiguous zero-count runs in a supplied ADC code histogram while excluding explicitly unexcited endpoint codes. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /runStarts/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=adc-missing-code-run-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "counts": [
        0,
        2,
        0,
        0,
        3,
        0
      ],
      "firstExcited": 1,
      "lastExcited": 4,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/runStarts": [
    2
  ],
  "/records/0/runLengths": [
    2
  ],
  "/records/0/missingCodes": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/runStarts/0",
  "/records/0/comparisonAvailable": true
}
```

## Adc Sinad Effective Bits Record

Service ID: `adc-sinad-effective-bits-record`. USD 9.00 per job.

Reconcile separated sinusoidal signal, noise and harmonic powers with the declared full-scale correction and ENOB convention. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /sinadDb using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=adc-sinad-effective-bits-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "signalPower": 100,
      "noisePower": 0.5,
      "harmonicPower": 0.5,
      "backoffDb": 0,
      "reportedValue": 20,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/sinadDb": 20,
  "/records/0/snrDb": 23.010299956639813,
  "/records/0/enob": 3.0299003322259135,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/sinadDb",
  "/records/0/comparisonAvailable": true
}
```

## Dac Bit Toggle Transfer Reconstruction Record

Service ID: `dac-bit-toggle-transfer-reconstruction-record`. USD 9.00 per job.

Reconstruct a bounded binary DAC transfer from independently measured bit-toggle weights and offset, retaining every transition DNL and nonmonotone transition count. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /codeV/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dac-bit-toggle-transfer-reconstruction-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "bitWeightV": [
        1,
        2,
        4
      ],
      "offsetV": 0,
      "nominalLsbV": 1,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/codeV": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7
  ],
  "/records/0/dnl": [
    0,
    0,
    0,
    0,
    0,
    0,
    0
  ],
  "/records/0/nonmonotoneTransitions": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/codeV/0",
  "/records/0/comparisonAvailable": true
}
```

## Dac Glitch Impulse Area Record

Service ID: `dac-glitch-impulse-area-record`. USD 9.00 per job.

Reconcile signed and absolute glitch areas from an explicitly baseline-subtracted piecewise-linear transient. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /signedVS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dac-glitch-impulse-area-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "volts": [
        0,
        2,
        0
      ],
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/signedVS": 2,
  "/records/0/absoluteVS": 2,
  "/records/0/peakV": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/signedVS",
  "/records/0/comparisonAvailable": true
}
```

## Pwm Pulse Level Average Record

Service ID: `pwm-pulse-level-average-record`. USD 9.00 per job.

Reconcile a repeating two-level measured pulse using separate high/low durations and voltage levels. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /duty using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pwm-pulse-level-average-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "highS": 1,
      "lowS": 3,
      "highV": 4,
      "lowV": 0,
      "reportedValue": 0.25,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/duty": 0.25,
  "/records/0/frequencyHz": 0.25,
  "/records/0/averageV": 1,
  "/records/0/rmsV": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/duty",
  "/records/0/comparisonAvailable": true
}
```

## Halfbridge Gate Deadtime Record

Service ID: `halfbridge-gate-deadtime-record`. USD 9.00 per job.

Reconcile one bounded switching period of two declared gate intervals into overlap, uncommanded gap and commanded duty. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /overlapS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=halfbridge-gate-deadtime-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "periodS": 10,
      "highStartS": 1,
      "highEndS": 4,
      "lowStartS": 5,
      "lowEndS": 9,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/overlapS": 0,
  "/records/0/gapS": 3,
  "/records/0/highDuty": 0.3,
  "/records/0/lowDuty": 0.4,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/overlapS",
  "/records/0/comparisonAvailable": true
}
```

## Switching Device Loss Ledger Record

Service ID: `switching-device-loss-ledger-record`. USD 9.00 per job.

Reconcile a declared rectangular-current switching scenario into conduction, overlap-switching and gate-charge loss contributions. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /conductionW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=switching-device-loss-ledger-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "currentA": 2,
      "onOhm": 1,
      "duty": 0.5,
      "busV": 10,
      "riseS": 0.1,
      "fallS": 0.1,
      "frequencyHz": 1,
      "gateC": 1,
      "gateV": 2,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/conductionW": 2,
  "/records/0/switchingW": 2,
  "/records/0/gateW": 2,
  "/records/0/totalW": 6,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/conductionW",
  "/records/0/comparisonAvailable": true
}
```

## Diode Reverse Recovery Waveform Record

Service ID: `diode-reverse-recovery-waveform-record`. USD 9.00 per job.

Integrate an explicitly nonpositive reverse-current pulse after its declared zero crossing and reconcile recovery charge and peak current. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /chargeC using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=diode-reverse-recovery-waveform-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "reverseA": [
        0,
        -2,
        0
      ],
      "blockingV": 3,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/chargeC": 2,
  "/records/0/peakA": 2,
  "/records/0/energyProxyJ": 6,
  "/records/0/peakTimeS": 1,
  "/records/0/recoveryDurationS": 2,
  "/records/0/softness": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/chargeC",
  "/records/0/comparisonAvailable": true
}
```

## Reservoir Capacitor Discharge Ripple Record

Service ID: `reservoir-capacitor-discharge-ripple-record`. USD 9.00 per job.

Reconcile exponential reservoir discharge between ideal instantaneous recharge events into droop and average capacitor voltage. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /valleyV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=reservoir-capacitor-discharge-ripple-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "peakV": 10,
      "resistanceOhm": 1,
      "capacitanceF": 1,
      "intervalS": 1,
      "reportedValue": 3.6787944117144233,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/valleyV": 3.6787944117144233,
  "/records/0/droopV": 6.321205588285577,
  "/records/0/averageV": 6.321205588285577,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/valleyV",
  "/records/0/comparisonAvailable": true
}
```

## Power Supply Line Load Separation Record

Service ID: `power-supply-line-load-separation-record`. USD 9.00 per job.

Resolve line and load sensitivities from an orthogonal three-observation supply test instead of conflating the two changes. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /lineVPerV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=power-supply-line-load-separation-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "baseInputV": 10,
      "changedInputV": 12,
      "baseLoadA": 1,
      "changedLoadA": 3,
      "baseOutputV": 5,
      "lineOutputV": 5.2,
      "loadOutputV": 4.8,
      "reportedValue": 0.1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/lineVPerV": 0.1,
  "/records/0/loadVPerA": -0.1,
  "/records/0/combinedPredictedV": 5,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/lineVPerV",
  "/records/0/comparisonAvailable": true
}
```

## Inductor Voltsecond Cycle Record

Service ID: `inductor-voltsecond-cycle-record`. USD 9.00 per job.

Reconcile a piecewise-constant inductor-voltage cycle into flux-linkage excursion and cycle volt-second imbalance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /endWbTurn using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=inductor-voltsecond-cycle-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "volts": [
        2,
        -1
      ],
      "durationsS": [
        1,
        2
      ],
      "initialWbTurn": 0,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/endWbTurn": 0,
  "/records/0/excursionWbTurn": 2,
  "/records/0/cycleVoltSeconds": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/endWbTurn",
  "/records/0/comparisonAvailable": true
}
```

## Transformer Flux Walk Record

Service ID: `transformer-flux-walk-record`. USD 9.00 per job.

Reconcile repeated measured cycle volt-seconds with winding turns and core area into signed accumulated flux-density drift. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /endTesla using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=transformer-flux-walk-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cycleVs": [
        1,
        -0.5,
        1
      ],
      "turns": 10,
      "areaM2": 0.1,
      "initialTesla": 0,
      "reportedValue": 1.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/endTesla": 1.5,
  "/records/0/peakAbsTesla": 1.5,
  "/records/0/trajectoryTesla": [
    1,
    0.5,
    1.5
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/endTesla",
  "/records/0/comparisonAvailable": true
}
```

## Closed Bh Loop Loss Record

Service ID: `closed-bh-loop-loss-record`. USD 9.00 per job.

Integrate an explicitly closed measured B-H polygon to signed loop energy density and positive cycle-loss magnitude. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /signedJPerM3 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=closed-bh-loop-loss-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "h": [
        0,
        1,
        1,
        0,
        0
      ],
      "b": [
        0,
        0,
        2,
        2,
        0
      ],
      "frequencyHz": 3,
      "volumeM3": 2,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/signedJPerM3": 2,
  "/records/0/lossJPerM3": 2,
  "/records/0/lossW": 12,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/signedJPerM3",
  "/records/0/comparisonAvailable": true
}
```

## Magnetic Core Loss Copper Subtraction Record

Service ID: `magnetic-core-loss-copper-subtraction-record`. USD 9.00 per job.

Separate supplied winding copper losses from AC input power at one measured excitation condition. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /copperW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=magnetic-core-loss-copper-subtraction-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputW": 20,
      "windingRmsA": [
        2,
        1
      ],
      "windingOhm": [
        1,
        2
      ],
      "coreKg": 2,
      "reportedValue": 6,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/copperW": 6,
  "/records/0/remainingW": 14,
  "/records/0/specificRemainingWPerKg": 7,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/copperW",
  "/records/0/comparisonAvailable": true
}
```

## Fuse Thermal Memory Current Record

Service ID: `fuse-thermal-memory-current-record`. USD 9.00 per job.

Reconcile a supplied piecewise-linear current history with a declared single-time-constant thermal-memory model, retaining thermal accumulation and uncooled squared-current exposure. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /terminalASquaredS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fuse-thermal-memory-current-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "amps": [
        1,
        1,
        1
      ],
      "coolingS": 1,
      "initialASquaredS": 0,
      "reportedValue": 0.8646647167633873,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/terminalASquaredS": 0.8646647167633873,
  "/records/0/thermalStates": [
    0.6321205588285577,
    0.8646647167633873
  ],
  "/records/0/uncooledASquaredS": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/terminalASquaredS",
  "/records/0/comparisonAvailable": true
}
```

## Contact Bounce Event Record

Service ID: `contact-bounce-event-record`. USD 9.00 per job.

Reconstruct contact state from ordered transition times, retaining bounce duration, transition count and closed dwell. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /transitions using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=contact-bounce-event-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        1,
        2,
        3
      ],
      "initialClosed": false,
      "endS": 5,
      "reportedValue": 3,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/transitions": 3,
  "/records/0/bounceSpanS": 2,
  "/records/0/closedS": 3,
  "/records/0/finalClosed": true,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/transitions",
  "/records/0/comparisonAvailable": true
}
```

## Relay Pickup Dropout Bracket Record

Service ID: `relay-pickup-dropout-bracket-record`. USD 9.00 per job.

Reconcile ordered voltage/state sweeps into bounded pickup and dropout transition brackets without interpolating an unseen switch point. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /pickupLowV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=relay-pickup-dropout-bracket-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "upV": [
        0,
        2,
        4
      ],
      "upOn": [
        false,
        false,
        true
      ],
      "downV": [
        4,
        2,
        0
      ],
      "downOn": [
        true,
        true,
        false
      ],
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/pickupLowV": 2,
  "/records/0/pickupHighV": 4,
  "/records/0/dropoutLowV": 0,
  "/records/0/dropoutHighV": 2,
  "/records/0/hysteresisLowV": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/pickupLowV",
  "/records/0/comparisonAvailable": true
}
```

## Relay Coil Thermal State Record

Service ID: `relay-coil-thermal-state-record`. USD 9.00 per job.

Reconcile a coil cold resistance and a later simultaneous voltage/current observation into resistance growth and temperature rise. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /hotOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=relay-coil-thermal-state-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "coldOhm": 10,
      "voltageV": 12,
      "currentA": 1,
      "coefficientPerK": 0.01,
      "reportedValue": 12,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/hotOhm": 12,
  "/records/0/riseK": 20,
  "/records/0/powerW": 12,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/hotOhm",
  "/records/0/comparisonAvailable": true
}
```

## Pcb Coupon Sheet Resistance Record

Service ID: `pcb-coupon-sheet-resistance-record`. USD 9.00 per job.

Reconcile four-terminal coupon measurements with declared trace geometry into resistivity, sheet resistance and coupon-to-coupon spread. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /resistivityOhmM/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pcb-coupon-sheet-resistance-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lengthM": [
        2,
        4
      ],
      "widthM": [
        1,
        1
      ],
      "thicknessM": [
        1,
        1
      ],
      "resistanceOhm": [
        4,
        8
      ],
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/resistivityOhmM": [
    2,
    2
  ],
  "/records/0/sheetOhm": [
    2,
    2
  ],
  "/records/0/relativeSpread": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/resistivityOhmM/0",
  "/records/0/comparisonAvailable": true
}
```

## Microphone Pistonphone Sensitivity Record

Service ID: `microphone-pistonphone-sensitivity-record`. USD 9.00 per job.

Reconcile a pistonphone pressure reference, microphone output and declared preamplifier gain into sensitivity and level. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /sensitivityVPerPa using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=microphone-pistonphone-sensitivity-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referencePa": 2,
      "outputV": 1,
      "preamplifierGain": 5,
      "reportedValue": 0.1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/sensitivityVPerPa": 0.1,
  "/records/0/sensitivityDb": -20,
  "/records/0/pressureLevelDb": 100,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/sensitivityVPerPa",
  "/records/0/comparisonAvailable": true
}
```

## Impedance Tube Two Microphone Record

Service ID: `impedance-tube-two-microphone-record`. USD 9.00 per job.

Reconstruct normal-incidence reflection from a supplied complex microphone transfer, spacing and reference distance under a plane-wave model. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /reflectionRe using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=impedance-tube-two-microphone-record) · [Technical reference](https://nptel.ac.in/courses/112104194)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "transferRe": 0,
      "transferIm": -0.3333333333333333,
      "kPerM": 1,
      "spacingM": 1.5707963267948966,
      "referenceM": 0,
      "reportedValue": 0.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/reflectionRe": 0.5,
  "/records/0/reflectionIm": 0,
  "/records/0/absorption": 0.75,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/reflectionRe",
  "/records/0/comparisonAvailable": true
}
```

## Standing Wave Tube Extrema Record

Service ID: `standing-wave-tube-extrema-record`. USD 9.00 per job.

Reconcile a pressure standing-wave maxima/minima pair into reflection magnitude, absorption and observed standing-wave ratio. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /reflectionMagnitude using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=standing-wave-tube-extrema-record) · [Technical reference](https://nptel.ac.in/courses/112104194)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "maxPa": 3,
      "minPa": 1,
      "reportedValue": 0.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/reflectionMagnitude": 0.5,
  "/records/0/absorption": 0.75,
  "/records/0/standingWaveRatio": 3,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/reflectionMagnitude",
  "/records/0/comparisonAvailable": true
}
```

## Sound Exposure Duration Ledger Record

Service ID: `sound-exposure-duration-ledger-record`. USD 9.00 per job.

Reconcile finite sound-level time blocks into energy-equivalent level and one-second-reference sound exposure level. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /leqDb using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sound-exposure-duration-ledger-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "levelDb": [
        0,
        10
      ],
      "seconds": [
        1,
        1
      ],
      "reportedValue": 7.403626894942439,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/leqDb": 7.403626894942439,
  "/records/0/exposureDb": 10.413926851582252,
  "/records/0/durationS": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/leqDb",
  "/records/0/comparisonAvailable": true
}
```

## Acoustic Band Background Subtraction Record

Service ID: `acoustic-band-background-subtraction-record`. USD 9.00 per job.

Subtract independently measured background energy in matched acoustic bands, retaining unresolved bands rather than manufacturing positive levels. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /netDb/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=acoustic-band-background-subtraction-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "totalDb": [
        10,
        10
      ],
      "backgroundDb": [
        0,
        10
      ],
      "reportedValue": 9.542425094393248,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/netDb": [
    9.542425094393248,
    null
  ],
  "/records/0/resolved": [
    true,
    false
  ],
  "/records/0/unresolvedBands": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/netDb/0",
  "/records/0/comparisonAvailable": true
}
```

## Sound Intensity Surface Power Record

Service ID: `sound-intensity-surface-power-record`. USD 9.00 per job.

Reconcile signed outward normal intensity observations over declared surface patches into net sound power and negative-flow share. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /netW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sound-intensity-surface-power-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "normalWPerM2": [
        2,
        -1
      ],
      "areaM2": [
        3,
        1
      ],
      "reportedValue": 5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/netW": 5,
  "/records/0/positiveW": 6,
  "/records/0/negativeMagnitudeW": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/netW",
  "/records/0/comparisonAvailable": true
}
```

## Reverberation Decay Line Record

Service ID: `reverberation-decay-line-record`. USD 9.00 per job.

Fit a supplied strictly decreasing decay-level interval and extrapolate its declared linear sixty-decibel decay time with fit residuals. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /slopeDbPerS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=reverberation-decay-line-record) · [Technical reference](https://nptel.ac.in/courses/112104194)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "levelDb": [
        0,
        -10,
        -20
      ],
      "reportedValue": -10,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/slopeDbPerS": -10,
  "/records/0/rt60S": 6,
  "/records/0/rmsResidualDb": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/slopeDbPerS",
  "/records/0/comparisonAvailable": true
}
```

## Microphone Comparator Transfer Record

Service ID: `microphone-comparator-transfer-record`. USD 9.00 per job.

Remove simultaneous source variation using matched reference and test microphone voltages at explicitly supplied frequencies. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /testVPerPa/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=microphone-comparator-transfer-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "frequencyHz": [
        100,
        1000
      ],
      "referenceV": [
        2,
        4
      ],
      "testV": [
        1,
        4
      ],
      "referenceVPerPa": [
        1,
        1
      ],
      "reportedValue": 0.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/testVPerPa": [
    0.5,
    1
  ],
  "/records/0/relativeDb": [
    -6.020599913279624,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/testVPerPa/0",
  "/records/0/comparisonAvailable": true
}
```

## Fractional Octave Tone Ledger Record

Service ID: `fractional-octave-tone-ledger-record`. USD 9.00 per job.

Assign supplied tonal mean-square pressures to exact base-two fractional-octave bands and retain unassigned energy. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /bandPa2/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fractional-octave-tone-ledger-record) · [Technical reference](https://nptel.ac.in/courses/112104194)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "frequencyHz": [
        100,
        200,
        1000
      ],
      "meanSquarePa2": [
        1,
        4,
        9
      ],
      "centersHz": [
        100,
        200
      ],
      "bandsPerOctave": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/bandPa2": [
    1,
    4
  ],
  "/records/0/unassignedPa2": 9,
  "/records/0/assignedTones": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/bandPa2/0",
  "/records/0/comparisonAvailable": true
}
```

## Accelerometer Back To Back Complex Record

Service ID: `accelerometer-back-to-back-complex-record`. USD 9.00 per job.

Reconcile complex reference/test sensor outputs with the declared reference sensitivity and conditioning gains. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /sensitivityReal using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=accelerometer-back-to-back-complex-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceReV": 2,
      "referenceImV": 0,
      "testReV": 0,
      "testImV": 4,
      "referenceSensitivity": 3,
      "referenceGain": 1,
      "testGain": 2,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/sensitivityReal": 0,
  "/records/0/sensitivityImag": 3,
  "/records/0/sensitivityMagnitude": 3,
  "/records/0/phaseRad": 1.5707963267948966,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/sensitivityReal",
  "/records/0/comparisonAvailable": true
}
```

## Laser Vibrometer Two Beam Record

Service ID: `laser-vibrometer-two-beam-record`. USD 9.00 per job.

Resolve two signed heterodyne Doppler observations along declared orthogonal axes into in-plane velocity and speed. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /velocityMPerS/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=laser-vibrometer-two-beam-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "beatHz": [
        4,
        6
      ],
      "offsetHz": [
        2,
        2
      ],
      "wavelengthM": 1,
      "cosine": [
        1,
        1
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/velocityMPerS": [
    1,
    2
  ],
  "/records/0/speedMPerS": 2.23606797749979,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/velocityMPerS/0",
  "/records/0/comparisonAvailable": true
}
```

## Accelerometer Cross Axis Matrix Record

Service ID: `accelerometer-cross-axis-matrix-record`. USD 9.00 per job.

Resolve a full three-axis sensitivity calibration from three independent applied acceleration vectors and matched voltage vectors. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /sensitivity/0/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=accelerometer-cross-axis-matrix-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "acceleration": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "voltage": [
        [
          2,
          0,
          0
        ],
        [
          0.1,
          3,
          0
        ],
        [
          0,
          0,
          4
        ]
      ],
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/sensitivity": [
    [
      2,
      0.1,
      0
    ],
    [
      0,
      3,
      0
    ],
    [
      0,
      0,
      4
    ]
  ],
  "/records/0/maximumCrossAxisFraction": 0.05,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/sensitivity/0/0",
  "/records/0/comparisonAvailable": true
}
```

## Charge Amplifier Decay Calibration Record

Service ID: `charge-amplifier-decay-calibration-record`. USD 9.00 per job.

Infer charge-amplifier feedback time constant from two same-polarity recovery voltages and compare injected charge with feedback capacitance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /timeConstantS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=charge-amplifier-decay-calibration-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "firstV": 4,
      "secondV": 2,
      "elapsedS": 1,
      "feedbackF": 2,
      "injectedC": 8,
      "reportedValue": 1.4426950408889634,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/timeConstantS": 1.4426950408889634,
  "/records/0/feedbackOhm": 0.7213475204444817,
  "/records/0/initialChargeResidualC": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/timeConstantS",
  "/records/0/comparisonAvailable": true
}
```

## Piezoelectric Force Pulse Charge Record

Service ID: `piezoelectric-force-pulse-charge-record`. USD 9.00 per job.

Integrate a baseline-corrected piecewise-linear piezoelectric current pulse into charge and force change under declared charge sensitivity. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /chargeC using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=piezoelectric-force-pulse-charge-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "currentA": [
        0,
        2,
        0
      ],
      "blankA": 0,
      "sensitivityCPerN": 0.5,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/chargeC": 2,
  "/records/0/forceChangeN": 4,
  "/records/0/peakCurrentA": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/chargeC",
  "/records/0/comparisonAvailable": true
}
```

## Lvdt Secondary Ratio Polynomial Record

Service ID: `lvdt-secondary-ratio-polynomial-record`. USD 9.00 per job.

Reconcile two demodulated secondary amplitudes with a declared odd cubic ratiometric displacement calibration. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /ratio using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lvdt-secondary-ratio-polynomial-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "firstV": 3,
      "secondV": 1,
      "linearM": 2,
      "cubicM": 0.5,
      "reportedValue": 0.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/ratio": 0.5,
  "/records/0/positionM": 1.0625,
  "/records/0/sumV": 4,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/ratio",
  "/records/0/comparisonAvailable": true
}
```

## Resolver Offset Gain Angle Record

Service ID: `resolver-offset-gain-angle-record`. USD 9.00 per job.

Reconcile resolver sine/cosine outputs after independently supplied channel offsets and gains, preserving magnitude and angle closure. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /angleRad using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=resolver-offset-gain-angle-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sineV": 3,
      "cosineV": 4,
      "sineOffsetV": 0,
      "cosineOffsetV": 0,
      "sineGain": 3,
      "cosineGain": 4,
      "referenceRad": 0.7853981633974483,
      "reportedValue": 0.7853981633974483,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/angleRad": 0.7853981633974483,
  "/records/0/magnitude": 1.4142135623730951,
  "/records/0/angleErrorRad": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/angleRad",
  "/records/0/comparisonAvailable": true
}
```

## Encoder Grid Cyclic Error Record

Service ID: `encoder-grid-cyclic-error-record`. USD 9.00 per job.

Reconcile a complete one-revolution encoder grid against uniform angular pitch after removing only the supplied datum. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /errorRad/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=encoder-grid-cyclic-error-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "angleRad": [
        0,
        1.7,
        3.141592653589793,
        4.7
      ],
      "datumRad": 0,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/errorRad": [
    0,
    0.1292036732051034,
    0,
    -0.012388980384689496
  ],
  "/records/0/peakToPeakRad": 0.1415926535897929,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/errorRad/0",
  "/records/0/comparisonAvailable": true
}
```

## Frequency Counter Allan Record

Service ID: `frequency-counter-allan-record`. USD 9.00 per job.

Reconcile contiguous equally gated fractional-frequency observations into overlapping Allan deviation across declared averaging factors. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /deviation/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=frequency-counter-allan-record) · [Technical reference](https://www.nist.gov/publications/handbook-frequency-stability-analysis)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "fractional": [
        1,
        1,
        1,
        1
      ],
      "factors": [
        1,
        2
      ],
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/deviation": [
    0,
    0
  ],
  "/records/0/pairs": [
    3,
    1
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/deviation/0",
  "/records/0/comparisonAvailable": true
}
```

## Frequency Counter Gate Weight Record

Service ID: `frequency-counter-gate-weight-record`. USD 9.00 per job.

Reconcile counter cycles over unequal positive contiguous gate durations into total-cycle frequency and arithmetic-mean bias. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /totalCycles using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=frequency-counter-gate-weight-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cycles": [
        10,
        30
      ],
      "gateS": [
        1,
        3
      ],
      "reportedValue": 40,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/totalCycles": 40,
  "/records/0/weightedHz": 10,
  "/records/0/unweightedHz": 10,
  "/records/0/weightingBiasHz": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/totalCycles",
  "/records/0/comparisonAvailable": true
}
```

## Heterodyne Frequency Ratio Record

Service ID: `heterodyne-frequency-ratio-record`. USD 9.00 per job.

Reconcile signed difference-frequency counts against a common reference and explicit mixer sideband for multiple channels. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /frequencyHz/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=heterodyne-frequency-ratio-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceHz": 100,
      "beatCycles": [
        10,
        20
      ],
      "gateS": [
        1,
        2
      ],
      "sideband": [
        1,
        -1
      ],
      "reportedValue": 110,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/frequencyHz": [
    110,
    90
  ],
  "/records/0/ratio": [
    1.1,
    0.9
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/frequencyHz/0",
  "/records/0/comparisonAvailable": true
}
```

## Pulse Top Droop Window Record

Service ID: `pulse-top-droop-window-record`. USD 9.00 per job.

Reconcile declared flat-top sample windows against a separate baseline into early/late levels and signed droop. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /earlyV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pulse-top-droop-window-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "baseline": [
        1,
        1
      ],
      "early": [
        5,
        5
      ],
      "late": [
        4,
        4
      ],
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/earlyV": 4,
  "/records/0/lateV": 3,
  "/records/0/droopV": 1,
  "/records/0/droopFraction": 0.25,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/earlyV",
  "/records/0/comparisonAvailable": true
}
```

## Photodiode Responsivity Quantum Record

Service ID: `photodiode-responsivity-quantum-record`. USD 9.00 per job.

Reconcile dark-subtracted photodiode current, wavelength and independently measured incident power into responsivity and external quantum efficiency. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /responsivityAPerW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=photodiode-responsivity-quantum-record) · [Technical reference](https://hub.hamamatsu.com/us/en/technical-notes/detector-selection/guide-to-detector-selection.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lightA": 3,
      "darkA": 1,
      "powerW": 2,
      "wavelengthM": 0.000001,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/responsivityAPerW": 1,
  "/records/0/externalQuantumEfficiency": 1.2398419843320025,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/responsivityAPerW",
  "/records/0/comparisonAvailable": true
}
```

## Integrating Sphere Port Substitution Record

Service ID: `integrating-sphere-port-substitution-record`. USD 9.00 per job.

Reconcile an ideal diffuse integrating-sphere substitution with explicitly supplied wall reflectance and port fractions. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /referenceMultiplier using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=integrating-sphere-port-substitution-record) · [Technical reference](https://www.labsphere.com/wp-content/uploads/2021/09/Integrating-Sphere-Theory-and-Applications.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceSignal": 2,
      "testSignal": 3,
      "referenceFluxW": 4,
      "wallReflectance": 0.8,
      "referencePortFraction": 0.1,
      "testPortFraction": 0.2,
      "reportedValue": 2.857142857142857,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/referenceMultiplier": 2.857142857142857,
  "/records/0/testMultiplier": 2.2222222222222223,
  "/records/0/testFluxW": 7.714285714285714,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/referenceMultiplier",
  "/records/0/comparisonAvailable": true
}
```

## Spectrometer Stray Light Matrix Record

Service ID: `spectrometer-stray-light-matrix-record`. USD 9.00 per job.

Reconcile a supplied two-band linear stray-light coupling model and retain nonphysical corrected intensity evidence as rejection. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /corrected/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=spectrometer-stray-light-matrix-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "measured": [
        12,
        21
      ],
      "coupling12": 0.1,
      "coupling21": 0.1,
      "reportedValue": 10,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/corrected": [
    10,
    20
  ],
  "/records/0/strayContributions": [
    2,
    1
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/corrected/0",
  "/records/0/comparisonAvailable": true
}
```

## Spectrometer Three Line Curvature Record

Service ID: `spectrometer-three-line-curvature-record`. USD 9.00 per job.

Resolve a quadratic wavelength calibration from three equally spaced detector reference locations and retain local dispersion at the middle location. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /coefficients/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=spectrometer-three-line-curvature-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pixel0": 0,
      "pixelStep": 1,
      "wavelength": [
        2,
        4,
        8
      ],
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coefficients": [
    2,
    1,
    1
  ],
  "/records/0/middleDispersion": 3,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/coefficients/0",
  "/records/0/comparisonAvailable": true
}
```

## Illuminance Distance Cosine Record

Service ID: `illuminance-distance-cosine-record`. USD 9.00 per job.

Reconcile measured illuminance observations at declared distances and incidence cosines into per-observation intensity and observed spread. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /candela/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=illuminance-distance-cosine-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lux": [
        2,
        0.5
      ],
      "distanceM": [
        1,
        2
      ],
      "cosine": [
        1,
        1
      ],
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/candela": [
    2,
    2
  ],
  "/records/0/meanCandela": 2,
  "/records/0/relativeSpread": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/candela/0",
  "/records/0/comparisonAvailable": true
}
```

## Stokes Five Channel Observation Record

Service ID: `stokes-five-channel-observation-record`. USD 9.00 per job.

Reconcile four linear analyzer intensities and one right-circular analyzer observation into a declared Stokes convention and polarization degree. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /stokes/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=stokes-five-channel-observation-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "i0": 3,
      "i45": 2,
      "i90": 1,
      "i135": 2,
      "iRight": 2,
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/stokes": [
    4,
    2,
    0,
    0
  ],
  "/records/0/degree": 0.5,
  "/records/0/linearAzimuthRad": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/stokes/0",
  "/records/0/comparisonAvailable": true
}
```

## Optical Extinction Dark Floor Record

Service ID: `optical-extinction-dark-floor-record`. USD 9.00 per job.

Reconcile dark-subtracted analyzer maximum/minimum powers and retain unresolved extinction when the minimum is at the dark floor. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /maximumNetW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=optical-extinction-dark-floor-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "maximumW": 11,
      "minimumW": 2,
      "darkW": 1,
      "reportedValue": 10,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/maximumNetW": 10,
  "/records/0/minimumNetW": 1,
  "/records/0/extinctionRatio": 10,
  "/records/0/extinctionDb": 10,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/maximumNetW",
  "/records/0/comparisonAvailable": true
}
```

## Neutral Density Stack Closure Record

Service ID: `neutral-density-stack-closure-record`. USD 9.00 per job.

Reconcile independently measured passive filter transmissions with a measured stacked transmission in both optical-density and multiplicative bases. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /expectedTransmission using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=neutral-density-stack-closure-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "transmission": [
        0.5,
        0.2
      ],
      "stacked": 0.1,
      "reportedValue": 0.1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/expectedTransmission": 0.1,
  "/records/0/expectedDensity": 1,
  "/records/0/stackDensityResidual": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/expectedTransmission",
  "/records/0/comparisonAvailable": true
}
```

## Photodiode Pulse Energy Waveform Record

Service ID: `photodiode-pulse-energy-waveform-record`. USD 9.00 per job.

Reconcile a dark-offset photodiode voltage transient with load resistance and responsivity into pulse energy, peak power and equivalent duration. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /energyJ using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=photodiode-pulse-energy-waveform-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "volts": [
        1,
        3,
        1
      ],
      "darkV": 1,
      "loadOhm": 2,
      "responsivity": 0.5,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/energyJ": 2,
  "/records/0/peakW": 2,
  "/records/0/equivalentDurationS": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/energyJ",
  "/records/0/comparisonAvailable": true
}
```

## Interferometer Quadrature Normalization Record

Service ID: `interferometer-quadrature-normalization-record`. USD 9.00 per job.

Normalize independently calibrated quadrature offsets/gains and reconcile a bounded sequence of interferometric phases and radius errors. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /phaseRad/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=interferometer-quadrature-normalization-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": [
        2,
        0,
        -2
      ],
      "y": [
        0,
        1,
        0
      ],
      "xOffset": 0,
      "yOffset": 0,
      "xGain": 2,
      "yGain": 1,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/phaseRad": [
    0,
    1.5707963267948966,
    3.141592653589793
  ],
  "/records/0/radiusError": [
    0,
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/phaseRad/0",
  "/records/0/comparisonAvailable": true
}
```

## Michelson Fringe Path Ledger Record

Service ID: `michelson-fringe-path-ledger-record`. USD 9.00 per job.

Reconcile signed fringe counts over multiple mirror strokes into apparent wavelength and closure against a declared air refractive index. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /vacuumWavelengthM/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=michelson-fringe-path-ledger-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "strokesM": [
        1,
        2
      ],
      "fringes": [
        2,
        4
      ],
      "airIndex": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/vacuumWavelengthM": [
    1,
    1
  ],
  "/records/0/meanWavelengthM": 1,
  "/records/0/spreadM": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/vacuumWavelengthM/0",
  "/records/0/comparisonAvailable": true
}
```

## Knife Edge Gaussian Width Record

Service ID: `knife-edge-gaussian-width-record`. USD 9.00 per job.

Reconcile measured 10-to-90-percent knife-edge transition locations along two axes into Gaussian second-moment beam diameters. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /d4SigmaXM using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=knife-edge-gaussian-width-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x10M": 0,
      "x90M": 2.5631031310892007,
      "y10M": 0,
      "y90M": 5.126206262178401,
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/d4SigmaXM": 4,
  "/records/0/d4SigmaYM": 8,
  "/records/0/ellipticity": 0.5,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/d4SigmaXM",
  "/records/0/comparisonAvailable": true
}
```

## Encircled Energy Radius Record

Service ID: `encircled-energy-radius-record`. USD 9.00 per job.

Reconcile nonnegative ring-integrated optical energies into cumulative fractions and a linearly bracketed requested energy radius. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /cumulativeFraction/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=encircled-energy-radius-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "outerRadiusM": [
        1,
        2,
        3
      ],
      "ringEnergy": [
        1,
        2,
        1
      ],
      "fraction": 0.5,
      "reportedValue": 0.25,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/cumulativeFraction": [
    0.25,
    0.75,
    1
  ],
  "/records/0/radiusM": 1.5,
  "/records/0/totalEnergy": 4,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/cumulativeFraction/0",
  "/records/0/comparisonAvailable": true
}
```

## Edge Spread Mtf Observation Record

Service ID: `edge-spread-mtf-observation-record`. USD 9.00 per job.

Differentiate a supplied uniformly spaced edge-spread trace into interval line-spread samples and normalized frequency-response magnitudes. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /lineSpread/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=edge-spread-mtf-observation-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "edge": [
        0,
        0.5,
        1
      ],
      "spacingM": 1,
      "frequencyPerM": [
        0,
        0.5
      ],
      "reportedValue": 0.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/lineSpread": [
    0.5,
    0.5
  ],
  "/records/0/mtf": [
    1,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/lineSpread/0",
  "/records/0/comparisonAvailable": true
}
```

## Camera Photon Transfer Pair Record

Service ID: `camera-photon-transfer-pair-record`. USD 9.00 per job.

Reconcile paired flat-field frame means and difference variances after a declared dark offset into shot-noise conversion gain and read-noise intercept. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /electronsPerDn using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=camera-photon-transfer-pair-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "signalDn": [
        1,
        2,
        3
      ],
      "differenceVarianceDn2": [
        4,
        6,
        8
      ],
      "darkDn": 0,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/electronsPerDn": 1,
  "/records/0/readNoiseDn": 1,
  "/records/0/slopeVariancePerDn": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/electronsPerDn",
  "/records/0/comparisonAvailable": true
}
```

## Camera Dark Current Exposure Record

Service ID: `camera-dark-current-exposure-record`. USD 9.00 per job.

Reconcile dark-frame charge accumulation across exposure durations after separately supplied bias and conversion gain; retain per-interval current and nonlinearity. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /currentElectronsPerS/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=camera-dark-current-exposure-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "exposureS": [
        1,
        2,
        3
      ],
      "meanDn": [
        3,
        5,
        7
      ],
      "biasDn": 1,
      "electronsPerDn": 2,
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/currentElectronsPerS": [
    4,
    4,
    4
  ],
  "/records/0/meanCurrent": 4,
  "/records/0/relativeSpread": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/currentElectronsPerS/0",
  "/records/0/comparisonAvailable": true
}
```

## Ccd Deferred Charge Trail Record

Service ID: `ccd-deferred-charge-trail-record`. USD 9.00 per job.

Reconcile a bright packet and its nonnegative deferred-charge trail into measured first-order transfer inefficiency and recovered-charge fraction. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /inefficiencyPerTransfer using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ccd-deferred-charge-trail-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "packetElectrons": 100,
      "trailElectrons": [
        2,
        1
      ],
      "transfers": 10,
      "reportedValue": 0.002,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/inefficiencyPerTransfer": 0.002,
  "/records/0/recoveredFraction": 0.02912621359223301,
  "/records/0/trailSumElectrons": 3,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/inefficiencyPerTransfer",
  "/records/0/comparisonAvailable": true
}
```

## Detector Nonparalyzable Deadtime Record

Service ID: `detector-nonparalyzable-deadtime-record`. USD 9.00 per job.

Reconcile observed count rates and declared nonparalyzable dead time into corrected rates and live fractions per supplied interval. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /observedHz/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=detector-nonparalyzable-deadtime-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "counts": [
        10,
        20
      ],
      "seconds": [
        1,
        2
      ],
      "deadS": 0.01,
      "reportedValue": 10,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/observedHz": [
    10,
    10
  ],
  "/records/0/correctedHz": [
    11.11111111111111,
    11.11111111111111
  ],
  "/records/0/liveFraction": [
    0.9,
    0.9
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/observedHz/0",
  "/records/0/comparisonAvailable": true
}
```

## Detector Paralyzable Lower Branch Record

Service ID: `detector-paralyzable-lower-branch-record`. USD 9.00 per job.

Reconcile observed rates under an explicit paralyzable lower-rate branch using bounded bisection, retaining occupancy and model residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /correctedHz using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=detector-paralyzable-lower-branch-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "observedHz": 0,
      "deadS": 1,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/correctedHz": 0,
  "/records/0/occupancy": 0,
  "/records/0/residualHz": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/correctedHz",
  "/records/0/comparisonAvailable": true
}
```

## Photon Bin Occupancy Correction Record

Service ID: `photon-bin-occupancy-correction-record`. USD 9.00 per job.

Reconcile repeated binary occupied-bin counts into Poisson arrivals per excitation opportunity and unresolved saturation flags. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /arrivalsPerOpportunity/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=photon-bin-occupancy-correction-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "occupied": [
        0,
        5
      ],
      "opportunities": [
        10,
        10
      ],
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/arrivalsPerOpportunity": [
    0,
    0.6931471805599453
  ],
  "/records/0/occupancy": [
    0,
    0.5
  ],
  "/records/0/saturated": [
    false,
    false
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/arrivalsPerOpportunity/0",
  "/records/0/comparisonAvailable": true
}
```

## Scintillator Two Line Energy Observation Record

Service ID: `scintillator-two-line-energy-observation-record`. USD 9.00 per job.

Reconcile a supplied affine detector channel-to-energy calibration with measured peak widths into centroids and fractional energy resolution. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /energyPerChannel using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=scintillator-two-line-energy-observation-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceChannels": [
        10,
        20
      ],
      "referenceEnergy": [
        100,
        300
      ],
      "peakChannels": [
        15
      ],
      "fwhmChannels": [
        2
      ],
      "reportedValue": 20,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/energyPerChannel": 20,
  "/records/0/offsetEnergy": -100,
  "/records/0/peakEnergy": [
    200
  ],
  "/records/0/fractionalResolution": [
    0.2
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/energyPerChannel",
  "/records/0/comparisonAvailable": true
}
```

## Photodiode Shot Thermal Noise Record

Service ID: `photodiode-shot-thermal-noise-record`. USD 9.00 per job.

Reconcile independent shot and resistor thermal current-noise variances over a declared equivalent noise bandwidth. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /shotASquared using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=photodiode-shot-thermal-noise-record) · [Technical reference](https://hub.hamamatsu.com/us/en/technical-notes/detector-selection/guide-to-detector-selection.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "photocurrentA": 1,
      "darkA": 0,
      "resistanceOhm": 1,
      "temperatureK": 1,
      "bandwidthHz": 1,
      "reportedValue": 3.204353268e-19,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/shotASquared": 3.204353268e-19,
  "/records/0/thermalASquared": 5.522596e-23,
  "/records/0/totalRmsA": 5.661188503839101e-10,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/shotASquared",
  "/records/0/comparisonAvailable": true
}
```

## Transimpedance Noise Gain Record

Service ID: `transimpedance-noise-gain-record`. USD 9.00 per job.

Reconcile ideal feedback impedance and input-capacitance noise gain at one supplied angular frequency. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /transimpedanceMagnitudeOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=transimpedance-noise-gain-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "feedbackOhm": 2,
      "feedbackF": 1,
      "inputF": 1,
      "omegaRadPerS": 0,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/transimpedanceMagnitudeOhm": 2,
  "/records/0/noiseGainMagnitude": 1,
  "/records/0/noiseGainReal": 1,
  "/records/0/noiseGainImag": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/transimpedanceMagnitudeOhm",
  "/records/0/comparisonAvailable": true
}
```

## Injection Capacitor Charge Calibration Record

Service ID: `injection-capacitor-charge-calibration-record`. USD 9.00 per job.

Reconcile multiple declared calibration-capacitor voltage steps with measured charge-amplifier output changes into gain and signed charge closure. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /injectedC/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=injection-capacitor-charge-calibration-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "calibrationF": 2,
      "inputStepV": [
        1,
        -1
      ],
      "outputStepV": [
        4,
        -4
      ],
      "declaredVPerC": 2,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/injectedC": [
    2,
    -2
  ],
  "/records/0/observedVPerC": [
    2,
    2
  ],
  "/records/0/outputResidualV": [
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/injectedC/0",
  "/records/0/comparisonAvailable": true
}
```

## Lockin Reference Phase Observation Record

Service ID: `lockin-reference-phase-observation-record`. USD 9.00 per job.

Rotate supplied in-phase/quadrature observations by a declared reference correction, preserving amplitude and signed phase. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /rotatedX using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lockin-reference-phase-observation-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": 3,
      "y": 4,
      "referenceCorrectionRad": 0,
      "reportedValue": 3,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/rotatedX": 3,
  "/records/0/rotatedY": 4,
  "/records/0/amplitude": 5,
  "/records/0/phaseRad": 0.9272952180016122,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/rotatedX",
  "/records/0/comparisonAvailable": true
}
```

## Excitation Reversal Commonmode Record

Service ID: `excitation-reversal-commonmode-record`. USD 9.00 per job.

Separate bridge differential response, excitation-even offset and common-mode leakage using two excitation polarities and independent common-mode gain. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /oddV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=excitation-reversal-commonmode-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "plusV": 3,
      "minusV": -1,
      "excitationV": 2,
      "commonModeV": 1,
      "commonModeGain": 0.5,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/oddV": 2,
  "/records/0/evenV": 1,
  "/records/0/correctedOddPerV": 1,
  "/records/0/unexplainedEvenV": 0.5,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/oddV",
  "/records/0/comparisonAvailable": true
}
```

## Oscilloscope Driven Channel Crosstalk Record

Service ID: `oscilloscope-driven-channel-crosstalk-record`. USD 9.00 per job.

Reconcile a measured voltage matrix from one-channel-at-a-time excitation into normalized crosstalk, diagonal gains and largest off-diagonal coupling. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /gain/0/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=oscilloscope-driven-channel-crosstalk-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "driveV": [
        1,
        2
      ],
      "measuredV": [
        [
          2,
          0.2
        ],
        [
          0.1,
          6
        ]
      ],
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gain": [
    [
      2,
      0.1
    ],
    [
      0.1,
      3
    ]
  ],
  "/records/0/worstOffDiagonal": 0.1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/gain/0/0",
  "/records/0/comparisonAvailable": true
}
```

## Tdr Step Impedance Reconstruction Record

Service ID: `tdr-step-impedance-reconstruction-record`. USD 9.00 per job.

Deconvolve a supplied finite incident/reflected trace pair into a causal reflection impulse, integrate its step reflection and reconstruct a positive-real impedance/distance profile. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /reflectionImpulse/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=tdr-step-impedance-reconstruction-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "incidentV": [
        1,
        1,
        1
      ],
      "reflectedV": [
        0,
        0.5,
        0.5
      ],
      "sampleS": 1,
      "propagationMPerS": 2,
      "referenceOhm": 1,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/reflectionImpulse": [
    0,
    0.5,
    0
  ],
  "/records/0/stepReflection": [
    0,
    0.5,
    0.5
  ],
  "/records/0/impedanceOhm": [
    1,
    3,
    3
  ],
  "/records/0/distanceM": [
    0,
    1,
    2
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/reflectionImpulse/0",
  "/records/0/comparisonAvailable": true
}
```

## Vna Oneport Error Calibration Record

Service ID: `vna-oneport-error-calibration-record`. USD 9.00 per job.

Resolve a one-port three-term complex error model from three distinct supplied standards and correct one DUT reflection. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /directivityRe using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=vna-oneport-error-calibration-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "standardRe": [
        -1,
        0,
        1
      ],
      "standardIm": [
        0,
        0,
        0
      ],
      "measuredRe": [
        -1,
        0,
        1
      ],
      "measuredIm": [
        0,
        0,
        0
      ],
      "dutRe": 0.5,
      "dutIm": 0,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/directivityRe": 0,
  "/records/0/directivityIm": 0,
  "/records/0/trackingRe": 1,
  "/records/0/trackingIm": 0,
  "/records/0/sourceMatchRe": 0,
  "/records/0/sourceMatchIm": 0,
  "/records/0/correctedRe": 0.5,
  "/records/0/correctedIm": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/directivityRe",
  "/records/0/comparisonAvailable": true
}
```

## Rf Square Law Detector Record

Service ID: `rf-square-law-detector-record`. USD 9.00 per job.

Reconcile a noise-offset square-law RF detector calibration with two supplied power references and a DUT voltage observation. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /voltsPerW using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rf-square-law-detector-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "powerW": [
        1,
        3
      ],
      "detectorV": [
        3,
        7
      ],
      "noiseV": 1,
      "dutV": 5,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/voltsPerW": 2,
  "/records/0/offsetResidualV": 0,
  "/records/0/dutW": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/voltsPerW",
  "/records/0/comparisonAvailable": true
}
```

## Matched Pi Attenuator Resistor Record

Service ID: `matched-pi-attenuator-resistor-record`. USD 9.00 per job.

Reconcile an ideal symmetric matched pi attenuator design with supplied measured shunt/series resistances and one reference impedance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /requiredShuntOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=matched-pi-attenuator-resistor-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceOhm": 1,
      "voltageAttenuation": 3,
      "measuredShuntOhm": 2,
      "measuredSeriesOhm": 1.3333333333333333,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/requiredShuntOhm": 2,
  "/records/0/requiredSeriesOhm": 1.3333333333333333,
  "/records/0/shuntResidualOhm": 0,
  "/records/0/seriesResidualOhm": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/requiredShuntOhm",
  "/records/0/comparisonAvailable": true
}
```

## Van Der Pauw Sheet Resistance Record

Service ID: `van-der-pauw-sheet-resistance-record`. USD 9.00 per job.

Resolve sheet resistance from two positive orthogonal van der Pauw observations and retain the defining exponential equation residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /sheetOhm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=van-der-pauw-sheet-resistance-record) · [Technical reference](https://www.nist.gov/pml/nanoscale-device-characterization-division/popular-links/hall-effect/resistivity-and-hall)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "resistanceA": 1,
      "resistanceB": 1,
      "thicknessM": 2,
      "reportedValue": 4.532360141827194,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/sheetOhm": 4.532360141827194,
  "/records/0/resistivityOhmM": 9.064720283654388,
  "/records/0/equationResidual": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/sheetOhm",
  "/records/0/comparisonAvailable": true
}
```

## Constant Strain Triangle Plane Stress Element

Service ID: `constant-strain-triangle-plane-stress-element`. USD 1.00 per job.

Construct the six-degree-of-freedom constant-strain triangular plane-stress elasticity element from supplied Cartesian nodes and isotropic material parameters. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=constant-strain-triangle-plane-stress-element) · [Technical reference](https://engcourses-uofa.ca/finite-element-analysis/two-dimensional-solid-elements/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "nodes": [
        [
          0,
          0
        ],
        [
          1,
          0
        ],
        [
          0,
          1
        ]
      ],
      "youngPa": 1,
      "poisson": 0,
      "thicknessM": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/areaM2": 0.5,
  "/records/0/stiffness": [
    [
      0.75,
      0.25,
      -0.5,
      -0.25,
      -0.25,
      0
    ],
    [
      0.25,
      0.75,
      0,
      -0.25,
      -0.25,
      -0.5
    ],
    [
      -0.5,
      0,
      0.5,
      0,
      0,
      0
    ],
    [
      -0.25,
      -0.25,
      0,
      0.25,
      0.25,
      0
    ],
    [
      -0.25,
      -0.25,
      0,
      0.25,
      0.25,
      0
    ],
    [
      0,
      -0.5,
      0,
      0,
      0,
      0.5
    ]
  ]
}
```

## Sallen Key Lowpass Pole Profile

Service ID: `sallen-key-lowpass-pole-profile`. USD 1.00 per job.

Resolve an ideal Sallen-Key equal-component lowpass into natural frequency, damping and its second-order step-response class. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sallen-key-lowpass-pole-profile) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "resistanceOhm": 1,
      "capacitanceF": 1,
      "gain": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/omega0": 1,
  "/records/0/quality": 0.5,
  "/records/0/damping": 1,
  "/records/0/stable": true
}
```

## Finite Opamp Feedback Pole

Service ID: `finite-opamp-feedback-pole`. USD 1.00 per job.

Resolve finite one-pole open-loop amplification with resistive feedback into closed-loop DC gain and pole, retaining gain error. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-opamp-feedback-pole) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "dcOpenGain": 99,
      "openPoleRadPerS": 1,
      "feedback": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/dcClosedGain": 0.99,
  "/records/0/closedPoleRadPerS": 100,
  "/records/0/relativeGainError": -0.01
}
```

## Opamp Offset Bias Superposition

Service ID: `opamp-offset-bias-superposition`. USD 1.00 per job.

Resolve the ideal noninverting amplifier output offset from differential offset voltage and two independently signed input bias currents. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=opamp-offset-bias-superposition) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "groundOhm": 1,
      "feedbackOhm": 3,
      "sourceOhm": 1,
      "offsetV": 1,
      "plusBiasA": 1,
      "minusBiasA": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/noiseGain": 4,
  "/records/0/offsetContributionV": 4,
  "/records/0/biasContributionV": -1,
  "/records/0/totalOffsetV": 3
}
```

## Difference Amplifier Resistor Mismatch

Service ID: `difference-amplifier-resistor-mismatch`. USD 1.00 per job.

Compute differential/common-mode gains for a four-resistor ideal difference amplifier and retain finite CMRR or its exact balanced singularity. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=difference-amplifier-resistor-mismatch) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "r1": 1,
      "r2": 2,
      "r3": 1,
      "r4": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/differentialGain": 2,
  "/records/0/commonGain": 0,
  "/records/0/cmrrDb": null
}
```

## Sar Ideal Conversion Trace

Service ID: `sar-ideal-conversion-trace`. USD 1.00 per job.

Replay a bounded unipolar successive-approximation conversion with its trial voltages and retained quantization interval. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sar-ideal-conversion-trace) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputV": 0.6,
      "referenceV": 1,
      "bits": 3
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/code": 4,
  "/records/0/trialCodes": [
    4,
    6,
    5
  ],
  "/records/0/trialVolts": [
    0.5,
    0.75,
    0.625
  ],
  "/records/0/lowerV": 0.5,
  "/records/0/upperV": 0.625
}
```

## Capacitive Dac Charge Sharing

Service ID: `capacitive-dac-charge-sharing`. USD 1.00 per job.

Resolve a floating common-node voltage after charge sharing across explicitly precharged capacitors and supplied bottom-plate shifts. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=capacitive-dac-charge-sharing) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "capacitanceF": [
        1,
        3
      ],
      "initialTopV": [
        1,
        1
      ],
      "initialBottomV": [
        0,
        0
      ],
      "finalBottomV": [
        0,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/finalTopV": 2.5,
  "/records/0/initialChargeC": 4,
  "/records/0/finalChargeC": 4,
  "/records/0/capacitorV": [
    2.5,
    0.5
  ]
}
```

## Switched Capacitor Settling Sequence

Service ID: `switched-capacitor-settling-sequence`. USD 1.00 per job.

Replay exact charge sharing followed by finite-RC acquisition for a supplied switched capacitor sample sequence. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=switched-capacitor-settling-sequence) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputV": [
        2,
        4
      ],
      "sampleF": 1,
      "holdF": 1,
      "onOhm": 1,
      "acquisitionS": 0,
      "initialHoldV": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/outputV": [
    0,
    0
  ],
  "/records/0/sharedV": [
    1,
    2
  ],
  "/records/0/finalHoldV": 0
}
```

## Series Rlc Initial Energy Response

Service ID: `series-rlc-initial-energy-response`. USD 1.00 per job.

Evaluate the exact underdamped unforced series-RLC capacitor voltage and current from arbitrary initial stored energy. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=series-rlc-initial-energy-response) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "resistanceOhm": 0,
      "inductanceH": 1,
      "capacitanceF": 1,
      "initialV": 1,
      "initialA": 0,
      "seconds": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/voltageV": 1,
  "/records/0/currentA": 0,
  "/records/0/storedJ": 0.5
}
```

## Mutually Coupled Inductor Energy

Service ID: `mutually-coupled-inductor-energy`. USD 1.00 per job.

Resolve flux linkages and stored magnetic energy of two passive reciprocal coupled inductors with a declared mutual sign. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mutually-coupled-inductor-energy) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "l1H": 2,
      "l2H": 2,
      "mutualH": 1,
      "i1A": 1,
      "i2A": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/linkage1": 4,
  "/records/0/linkage2": 5,
  "/records/0/energyJ": 7
}
```

## Ideal Buck Discontinuous State

Service ID: `ideal-buck-discontinuous-state`. USD 1.00 per job.

Resolve an ideal buck converter discontinuous-conduction cycle from supplied on-time, load, inductance and switching period. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ideal-buck-discontinuous-state) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputV": 10,
      "outputV": 5,
      "inductanceH": 1,
      "onS": 1,
      "periodS": 4
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/peakA": 5,
  "/records/0/offS": 1,
  "/records/0/zeroS": 2,
  "/records/0/averageA": 1.25,
  "/records/0/outputW": 6.25
}
```

## Ideal Boost Continuous Ripple

Service ID: `ideal-boost-continuous-ripple`. USD 1.00 per job.

Resolve ideal continuous-conduction boost current and output capacitor ripple under an explicit positive minimum-inductor-current condition. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ideal-boost-continuous-ripple) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputV": 5,
      "outputV": 10,
      "outputA": 1,
      "inductanceH": 1,
      "capacitanceF": 1,
      "frequencyHz": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/duty": 0.5,
  "/records/0/meanInductorA": 2,
  "/records/0/peakToPeakA": 0.25,
  "/records/0/minimumA": 1.875,
  "/records/0/capacitorRippleV": 0.05
}
```

## Flyback Magnetizing Energy Cycle

Service ID: `flyback-magnetizing-energy-cycle`. USD 1.00 per job.

Resolve an ideal isolated flyback discontinuous magnetizing cycle into peak primary current, secondary decay time and delivered energy. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=flyback-magnetizing-energy-cycle) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputV": 10,
      "outputV": 5,
      "primaryH": 1,
      "primaryToSecondary": 2,
      "onS": 1,
      "periodS": 4
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/primaryPeakA": 10,
  "/records/0/secondaryPeakA": 20,
  "/records/0/decayS": 1,
  "/records/0/energyJ": 50,
  "/records/0/averageW": 12.5
}
```

## Bjt Loaded Bias Dc Root

Service ID: `bjt-loaded-bias-dc-root`. USD 1.00 per job.

Solve an ideal forward-active BJT Thevenin base bias with emitter degeneration and reject saturation rather than silently using active equations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bjt-loaded-bias-dc-root) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "supplyV": 10,
      "theveninV": 2,
      "theveninOhm": 10,
      "emitterOhm": 1,
      "collectorOhm": 1,
      "beta": 9,
      "baseEmitterV": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/baseA": 0.05,
  "/records/0/collectorA": 0.45,
  "/records/0/emitterV": 0.5,
  "/records/0/collectorEmitterV": 9.05
}
```

## Mosfet Resistive Load Square Law

Service ID: `mosfet-resistive-load-square-law`. USD 1.00 per job.

Solve the ideal long-channel saturation square-law current with source degeneration and explicitly validate its drain saturation region. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mosfet-resistive-load-square-law) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gateV": 3,
      "thresholdV": 1,
      "kAPerV2": 2,
      "sourceOhm": 1,
      "drainOhm": 1,
      "supplyV": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/drainA": 1,
  "/records/0/overdriveV": 1,
  "/records/0/sourceV": 1,
  "/records/0/drainSourceV": 8
}
```

## Diode Bridge Resistive Waveform

Service ID: `diode-bridge-resistive-waveform`. USD 1.00 per job.

Evaluate full-wave bridge output samples with a declared fixed two-diode drop and a positive resistive load. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=diode-bridge-resistive-waveform) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputV": [
        0,
        3,
        -3
      ],
      "diodeDropV": 0.5,
      "loadOhm": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/outputV": [
    0,
    2,
    2
  ],
  "/records/0/loadA": [
    0,
    1,
    1
  ],
  "/records/0/meanLoadW": 1.3333333333333333
}
```

## Zener Piecewise Shunt Regulator

Service ID: `zener-piecewise-shunt-regulator`. USD 1.00 per job.

Resolve an explicit piecewise ideal Zener shunt regulator into off/on state, terminal voltage, load current and dissipation. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=zener-piecewise-shunt-regulator) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "supplyV": 10,
      "seriesOhm": 1,
      "loadOhm": 4,
      "zenerV": 4
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/outputV": 4,
  "/records/0/zenerA": 5,
  "/records/0/loadA": 1,
  "/records/0/zenerW": 20,
  "/records/0/regulating": true
}
```

## Resistive Bridge Thevenin Port

Service ID: `resistive-bridge-thevenin-port`. USD 1.00 per job.

Resolve an unloaded four-resistor bridge differential port into signed Thevenin voltage, resistance and arbitrary resistive load current. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=resistive-bridge-thevenin-port) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "r1": 1,
      "r2": 1,
      "r3": 1,
      "r4": 3,
      "sourceV": 8,
      "loadOhm": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/openV": 2,
  "/records/0/theveninOhm": 1.25,
  "/records/0/loadA": 0.8888888888888888,
  "/records/0/loadV": 0.8888888888888888
}
```

## Rc Ladder Elmore Moment

Service ID: `rc-ladder-elmore-moment`. USD 1.00 per job.

Compute Elmore delay moments to every node of an unbranched positive RC ladder with capacitors at downstream nodes. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rc-ladder-elmore-moment) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "resistanceOhm": [
        1,
        2
      ],
      "capacitanceF": [
        3,
        4
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/delayS": [
    7,
    15
  ],
  "/records/0/totalCapacitanceF": 7
}
```

## Transmission Line Twoport Abcd

Service ID: `transmission-line-twoport-abcd`. USD 1.00 per job.

Build a uniform lossy line complex ABCD two-port from explicit complex propagation-length and characteristic impedance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=transmission-line-twoport-abcd) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gammaLengthRe": 0,
      "gammaLengthIm": 1.5707963267948966,
      "z0Re": 2,
      "z0Im": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/a": [
    0,
    0
  ],
  "/records/0/b": [
    0,
    2
  ],
  "/records/0/c": [
    0,
    0.5
  ],
  "/records/0/d": [
    0,
    0
  ],
  "/records/0/determinant": [
    1,
    0
  ]
}
```

## Sparameter Twoport Transducer Gain

Service ID: `sparameter-twoport-transducer-gain`. USD 1.00 per job.

Compute two-port transducer power gain with explicit complex source/load reflections and reject nonpositive available-power factors. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sparameter-twoport-transducer-gain) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "s11": [
        0,
        0
      ],
      "s12": [
        0,
        0
      ],
      "s21": [
        2,
        0
      ],
      "s22": [
        0,
        0
      ],
      "source": [
        0,
        0
      ],
      "load": [
        0,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gain": 4,
  "/records/0/gainDb": 6.020599913279624,
  "/records/0/denominatorMagnitude": 1
}
```

## Rf Rollett Stability Factors

Service ID: `rf-rollett-stability-factors`. USD 1.00 per job.

Compute determinant and Rollett K plus both mu factors for an explicit complex two-port, reporting unconditional-stability inequalities as supplied-model evidence. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rf-rollett-stability-factors) · [Technical reference](https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Microwave_and_RF_Design_V:_Amplifiers_and_Oscillators_(Steer)/02:_Linear_Amplifiers/2.06:_Amplifier_Stability)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "s11": [
        0,
        0
      ],
      "s12": [
        0.1,
        0
      ],
      "s21": [
        2,
        0
      ],
      "s22": [
        0,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/delta": [
    -0.2,
    0
  ],
  "/records/0/k": 2.6,
  "/records/0/muInput": 5,
  "/records/0/muOutput": 5,
  "/records/0/unconditionallyStable": true
}
```

## Friis Cascade Noise Temperature

Service ID: `friis-cascade-noise-temperature`. USD 1.00 per job.

Resolve ordered linear amplifier gains and noise temperatures into equivalent input temperature and stage-referred contributions. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=friis-cascade-noise-temperature) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gains": [
        2,
        3
      ],
      "noiseK": [
        10,
        20
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/inputNoiseK": 20,
  "/records/0/stageReferredK": [
    10,
    10
  ],
  "/records/0/totalGain": 6
}
```

## Noise Correlation Complex Combination

Service ID: `noise-correlation-complex-combination`. USD 1.00 per job.

Combine two complex-correlated RMS noise sources with explicit phase-sensitive transfer coefficients and a valid coherence bound. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=noise-correlation-complex-combination) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "rms1": 3,
      "rms2": 4,
      "correlation": [
        0,
        0
      ],
      "gain1": [
        1,
        0
      ],
      "gain2": [
        1,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/variance": 25,
  "/records/0/rms": 5,
  "/records/0/crossVariance": 0
}
```

## Electrothermal Two Node Steady

Service ID: `electrothermal-two-node-steady`. USD 1.00 per job.

Solve a positive two-node thermal resistance network with separate heat inputs and ambient, retaining each heat path and node temperature. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=electrothermal-two-node-steady) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/10-3-kirchhoffs-rules)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "ambientK": 300,
      "r1KPerW": 1,
      "r2KPerW": 2,
      "couplingKPerW": 1,
      "p1W": 2,
      "p2W": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/temperatureK": [
    301.5,
    301
  ],
  "/records/0/ambientFlowW": [
    1.5,
    0.5
  ],
  "/records/0/couplingFlowW": 0.5
}
```

## Rectangular Pulse Fourier Series

Service ID: `rectangular-pulse-fourier-series`. USD 1.00 per job.

Compute complex Fourier-series coefficients of a shifted rectangular pulse train for explicit integer harmonics, including the exact DC branch. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rectangular-pulse-fourier-series) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "amplitude": 2,
      "duty": 0.5,
      "offsetCycles": 0,
      "harmonics": [
        0,
        1,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/real": [
    1,
    0,
    0
  ],
  "/records/0/imag": [
    0,
    -0.6366197723675814,
    0
  ]
}
```

## Barycentric Trigonometric Interpolation

Service ID: `barycentric-trigonometric-interpolation`. USD 1.00 per job.

Evaluate the unique odd-length periodic trigonometric interpolant on an equispaced cyclic grid using its cardinal sine kernel. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=barycentric-trigonometric-interpolation) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "samples": [
        1,
        1,
        1
      ],
      "phaseCycles": [
        0,
        0.1,
        0.5
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/values": [
    1,
    1,
    1
  ]
}
```

## Overlap Save Fir Block Plan

Service ID: `overlap-save-fir-block-plan`. USD 1.00 per job.

Construct actual overlap-save block windows and retained samples for a supplied FIR, preserving input/output index correspondence. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=overlap-save-fir-block-plan) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "signal": [
        1,
        2,
        3
      ],
      "kernel": [
        1,
        1
      ],
      "blockLength": 4
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/output": [
    1,
    3,
    5,
    3
  ],
  "/records/0/blockStarts": [
    -1,
    2
  ],
  "/records/0/validPerBlock": [
    3,
    1
  ]
}
```

## Linear Phase Fir Symmetry Class

Service ID: `linear-phase-fir-symmetry-class`. USD 1.00 per job.

Classify supplied real FIR exact symmetry into types I–IV and report forced zero constraints and group delay. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=linear-phase-fir-symmetry-class) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "kernel": [
        1,
        2,
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/type": "I",
  "/records/0/groupDelaySamples": 1,
  "/records/0/zeroAtDc": false,
  "/records/0/zeroAtNyquist": false
}
```

## Minimum Phase Root Reflection

Service ID: `minimum-phase-root-reflection`. USD 1.00 per job.

Reflect explicitly supplied nonzero FIR zero locations outside the unit circle and adjust gain to preserve unit-circle magnitude. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=minimum-phase-root-reflection) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "zerosRe": [
        2
      ],
      "zerosIm": [
        0
      ],
      "gain": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/zerosRe": [
    0.5
  ],
  "/records/0/zerosIm": [
    0
  ],
  "/records/0/gain": 2,
  "/records/0/reflected": 1
}
```

## Bilinear Analog Root Map

Service ID: `bilinear-analog-root-map`. USD 1.00 per job.

Map supplied stable analog pole/zero locations through a bilinear transform and append the exact infinity zeros needed by a proper transfer function. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bilinear-analog-root-map) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "polesRe": [
        -2
      ],
      "polesIm": [
        0
      ],
      "zerosRe": [],
      "zerosIm": [],
      "sampleRateHz": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/polesRe": [
    0
  ],
  "/records/0/polesIm": [
    0
  ],
  "/records/0/zerosRe": [
    -1
  ],
  "/records/0/zerosIm": [
    0
  ]
}
```

## Fractional Delay Lagrange Fir

Service ID: `fractional-delay-lagrange-fir`. USD 1.00 per job.

Construct a finite Lagrange fractional-delay FIR on consecutive sample nodes and retain polynomial-reproduction moment residuals. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fractional-delay-lagrange-fir) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "order": 2,
      "delaySamples": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/kernel": [
    0.375,
    0.75,
    -0.125
  ],
  "/records/0/momentResidual": [
    0,
    0,
    0
  ]
}
```

## Lattice Allpass Coefficient Recursion

Service ID: `lattice-allpass-coefficient-recursion`. USD 1.00 per job.

Build a real stable allpass numerator/denominator from supplied strict reflection coefficients by step-up recursion. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lattice-allpass-coefficient-recursion) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "reflection": [
        0.5
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/numerator": [
    0.5,
    1
  ],
  "/records/0/denominator": [
    1,
    0.5
  ]
}
```

## Haar Best K Term Reconstruction

Service ID: `haar-best-k-term-reconstruction`. USD 1.00 per job.

Construct a deterministic best-k-term orthonormal Haar approximation from coefficients, preserving approximation error energy and retained indices. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=haar-best-k-term-reconstruction) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "samples": [
        1,
        1,
        1,
        1
      ],
      "keep": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/reconstruction": [
    1,
    1,
    1,
    1
  ],
  "/records/0/retained": [
    0
  ],
  "/records/0/discardedEnergy": 0
}
```

## Dft Circular Sample Shift

Service ID: `dft-circular-sample-shift`. USD 1.00 per job.

Apply an exact integer circular shift to a supplied periodic sample vector and expose the corresponding selected Fourier phase multipliers. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dft-circular-sample-shift) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "samples": [
        1,
        2,
        3
      ],
      "shift": 1,
      "bins": [
        0,
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/shifted": [
    3,
    1,
    2
  ],
  "/records/0/phaseReal": [
    1,
    -0.5
  ],
  "/records/0/phaseImag": [
    0,
    -0.8660254037844386
  ]
}
```

## Periodic Discrete Difference Regularization

Service ID: `periodic-discrete-difference-regularization`. USD 1.00 per job.

Solve a periodic first-difference Tikhonov smoothing problem by diagonal Fourier filtering and report data/roughness costs. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=periodic-discrete-difference-regularization) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "samples": [
        1,
        1,
        1,
        1
      ],
      "lambda": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/smoothed": [
    1,
    1,
    1,
    1
  ],
  "/records/0/dataCost": 0,
  "/records/0/roughnessCost": 0
}
```

## Sampled Chirp Dechirp Correlation

Service ID: `sampled-chirp-dechirp-correlation`. USD 1.00 per job.

Dechirp a supplied complex observation against a deterministic linear-frequency reference and report coherent complex sum and residual envelope. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sampled-chirp-dechirp-correlation) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "real": [
        1,
        1
      ],
      "imag": [
        0,
        0
      ],
      "initialPhaseRad": 0,
      "cyclesPerSample": 0,
      "chirpPerSample2": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coherentReal": 2,
  "/records/0/coherentImag": 0,
  "/records/0/envelope": [
    1,
    1
  ]
}
```

## Complex Inphase Quadrature Imbalance

Service ID: `complex-inphase-quadrature-imbalance`. USD 1.00 per job.

Resolve an explicit widely-linear IQ imbalance model y=a*x+b*conj(x), reporting image-rejection ratio and invertibility. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=complex-inphase-quadrature-imbalance) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputRe": [
        1,
        0
      ],
      "inputIm": [
        0,
        1
      ],
      "a": [
        1,
        0
      ],
      "b": [
        0.5,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/outputRe": [
    1.5,
    0
  ],
  "/records/0/outputIm": [
    0,
    0.5
  ],
  "/records/0/imageRejection": 4,
  "/records/0/invertible": true
}
```

## Sampled Ambiguity Function Grid

Service ID: `sampled-ambiguity-function-grid`. USD 1.00 per job.

Compute a supplied complex baseband signal ambiguity function on explicit integer delays and normalized Doppler frequencies using finite zero padding. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sampled-ambiguity-function-grid) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "real": [
        1,
        1
      ],
      "imag": [
        0,
        0
      ],
      "delays": [
        0,
        1
      ],
      "doppler": [
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/power": [
    [
      4
    ],
    [
      1
    ]
  ]
}
```

## Stft Overlap Add Window Condition

Service ID: `stft-overlap-add-window-condition`. USD 1.00 per job.

Compute periodic overlap-add sums of a supplied analysis/synthesis window pair over the least repeating hop period and report exact nonzero reconstruction normalization. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=stft-overlap-add-window-condition) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "analysis": [
        1,
        1,
        1,
        1
      ],
      "synthesis": [
        1,
        1,
        1,
        1
      ],
      "hop": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/periodicSums": [
    2,
    2
  ],
  "/records/0/constant": true,
  "/records/0/normalization": [
    0.5,
    0.5
  ]
}
```

## Isoparametric Quadrilateral Shape Gradient

Service ID: `isoparametric-quadrilateral-shape-gradient`. USD 1.00 per job.

Resolve a supplied four-node bilinear Cartesian finite-element mapping into shape functions, physical gradients and local Jacobian at one natural-coordinate point. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=isoparametric-quadrilateral-shape-gradient) · [Technical reference](https://engcourses-uofa.ca/finite-element-analysis/two-dimensional-solid-elements/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "nodes": [
        [
          -1,
          -1
        ],
        [
          1,
          -1
        ],
        [
          1,
          1
        ],
        [
          -1,
          1
        ]
      ],
      "xi": 0,
      "eta": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/shape": [
    0.25,
    0.25,
    0.25,
    0.25
  ],
  "/records/0/gradient": [
    [
      -0.25,
      -0.25
    ],
    [
      0.25,
      -0.25
    ],
    [
      0.25,
      0.25
    ],
    [
      -0.25,
      0.25
    ]
  ],
  "/records/0/jacobian": [
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ],
  "/records/0/determinant": 1
}
```

## Discrete Minimax Polynomial Approximation

Service ID: `discrete-minimax-polynomial-approximation`. USD 1.00 per job.

Construct a discrete-grid minimax polynomial by exhaustive Chebyshev-alternation candidates, retaining its maximum supplied-grid error and extremal witness. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=discrete-minimax-polynomial-approximation) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": [
        -1,
        0,
        1
      ],
      "y": [
        1,
        0,
        1
      ],
      "degree": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coefficients": [
    0.5
  ],
  "/records/0/maximumError": 0.5,
  "/records/0/extremalIndices": [
    0,
    1
  ]
}
```

## Sampled Complex Coherence Frames

Service ID: `sampled-complex-coherence-frames`. USD 1.00 per job.

Reconcile corresponding complex spectral frame observations into auto/cross powers and magnitude-squared coherence for one bin. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sampled-complex-coherence-frames) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "xRe": [
        1,
        2
      ],
      "xIm": [
        0,
        0
      ],
      "yRe": [
        2,
        4
      ],
      "yIm": [
        0,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/crossReal": 5,
  "/records/0/crossImag": 0,
  "/records/0/xPower": 2.5,
  "/records/0/yPower": 10,
  "/records/0/coherence": 1
}
```

## Second Order Digital Notch Design

Service ID: `second-order-digital-notch-design`. USD 1.00 per job.

Construct a real second-order notch filter with explicit center frequency and pole radius, normalize DC gain and retain pole/zero locations. Factored representation with delay variable u is gainScale*((1-u)^2+2*cosineDefect*u)/((1-r*u)^2+2*r*cosineDefect*u), where r=1-radiusDefect. A coefficientResolutionLimited finding means twelve-significant-digit polynomial DC sums lose more than 1e-8 relative accuracy; use the factored representation. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=second-order-digital-notch-design) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cyclesPerSample": 0.25,
      "poleRadius": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/numerator": [
    0.625,
    0,
    0.625
  ],
  "/records/0/denominator": [
    1,
    0,
    0.25
  ],
  "/records/0/zeroAnglesRad": [
    1.5707963267948966,
    -1.5707963267948966
  ],
  "/records/0/gainScale": 0.625,
  "/records/0/cosineDefect": 1,
  "/records/0/radiusDefect": 0.5,
  "/records/0/coefficientResolutionLimited": false
}
```

## Weighted Graph Minimum Bisection

Service ID: `weighted-graph-minimum-bisection`. USD 1.00 per job.

Enumerate balanced vertex bipartitions of a small supplied symmetric nonnegative graph and return minimum cut weight with a deterministic witness. Off-diagonal zero graph/cost entries denote absent edges; all matrix indices are zero-based.  Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=weighted-graph-minimum-bisection) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          4,
          0
        ],
        [
          1,
          0,
          0,
          4
        ],
        [
          4,
          0,
          0,
          1
        ],
        [
          0,
          4,
          1,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/left": [
    0,
    2
  ],
  "/records/0/right": [
    1,
    3
  ],
  "/records/0/cutWeight": 2
}
```

## General Graph Weighted Matching Exact

Service ID: `general-graph-weighted-matching-exact`. USD 1.00 per job.

Find a maximum-weight matching in a small undirected graph without requiring bipartiteness; vertices may remain unmatched. Off-diagonal zero graph/cost entries denote absent edges; all matrix indices are zero-based.  Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=general-graph-weighted-matching-exact) · [Technical reference](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.matching.max_weight_matching.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          3,
          2
        ],
        [
          3,
          0,
          1
        ],
        [
          2,
          1,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/pairs": [
    [
      0,
      1
    ]
  ],
  "/records/0/weight": 3,
  "/records/0/unmatched": [
    2
  ]
}
```

## Undirected Minimum Weight Cycle Basis

Service ID: `undirected-minimum-weight-cycle-basis`. USD 1.00 per job.

Construct a minimum-total-weight independent cycle basis of a bounded undirected graph by enumerating simple cycle edge masks and greedy binary-matroid selection. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=undirected-minimum-weight-cycle-basis) · [Technical reference](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.cycles.minimum_cycle_basis.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          1
        ],
        [
          1,
          0,
          1
        ],
        [
          1,
          1,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/cycles": [
    [
      0,
      1,
      2
    ]
  ],
  "/records/0/totalWeight": 3,
  "/records/0/rank": 1
}
```

## Graph Minimum Fill Elimination

Service ID: `graph-minimum-fill-elimination`. USD 1.00 per job.

Enumerate elimination orders of a bounded undirected graph and return a minimum-fill chordal completion with recorded fill edges. Off-diagonal zero graph/cost entries denote absent edges; all matrix indices are zero-based.  Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=graph-minimum-fill-elimination) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          0,
          1
        ],
        [
          1,
          0,
          1,
          0
        ],
        [
          0,
          1,
          0,
          1
        ],
        [
          1,
          0,
          1,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/order": [
    0,
    1,
    2,
    3
  ],
  "/records/0/fillEdges": [
    [
      1,
      3
    ]
  ],
  "/records/0/fillCount": 1
}
```

## Graph Minimum Bandwidth Order

Service ID: `graph-minimum-bandwidth-order`. USD 1.00 per job.

Find a vertex ordering minimizing the largest index separation over supplied undirected edges, with exact bounded permutation enumeration. Off-diagonal zero graph/cost entries denote absent edges; all matrix indices are zero-based.  Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=graph-minimum-bandwidth-order) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          1
        ],
        [
          1,
          0,
          0
        ],
        [
          1,
          0,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/order": [
    1,
    0,
    2
  ],
  "/records/0/bandwidth": 1
}
```

## Weighted Minimum Linear Arrangement

Service ID: `weighted-minimum-linear-arrangement`. USD 1.00 per job.

Minimize the weighted sum of undirected edge lengths under a one-dimensional vertex arrangement, retaining per-edge costs. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=weighted-minimum-linear-arrangement) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          1
        ],
        [
          1,
          0,
          0
        ],
        [
          1,
          0,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/order": [
    1,
    0,
    2
  ],
  "/records/0/cost": 2,
  "/records/0/edgeCosts": [
    1,
    1
  ]
}
```

## Connected Dominating Set Exact

Service ID: `connected-dominating-set-exact`. USD 1.00 per job.

Find a minimum-cost connected dominating vertex set in a bounded graph, allowing only supplied nonnegative vertex costs. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=connected-dominating-set-exact) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          0
        ],
        [
          1,
          0,
          1
        ],
        [
          0,
          1,
          0
        ]
      ],
      "costs": [
        1,
        2,
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/vertices": [
    1
  ],
  "/records/0/cost": 2
}
```

## Terminal Vertex Separator Exact

Service ID: `terminal-vertex-separator-exact`. USD 1.00 per job.

Find a minimum-cost nonterminal vertex separator between two named vertices, explicitly rejecting an inseparable direct edge. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=terminal-vertex-separator-exact) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          0
        ],
        [
          1,
          0,
          1
        ],
        [
          0,
          1,
          0
        ]
      ],
      "costs": [
        9,
        2,
        9
      ],
      "source": 0,
      "target": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/separator": [
    1
  ],
  "/records/0/cost": 2
}
```

## Resource Constrained Elementary Path

Service ID: `resource-constrained-elementary-path`. USD 1.00 per job.

Find a least-cost simple directed path subject to one additive nonnegative resource budget by bounded complete path enumeration. Off-diagonal zero graph/cost entries denote absent edges; all matrix indices are zero-based.  Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=resource-constrained-elementary-path) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cost": [
        [
          0,
          1,
          5
        ],
        [
          0,
          0,
          1
        ],
        [
          0,
          0,
          0
        ]
      ],
      "resource": [
        [
          0,
          2,
          1
        ],
        [
          0,
          0,
          2
        ],
        [
          0,
          0,
          0
        ]
      ],
      "source": 0,
      "target": 2,
      "budget": 3
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/path": [
    0,
    2
  ],
  "/records/0/cost": 5,
  "/records/0/resource": 1,
  "/records/0/feasible": true
}
```

## Graph Terminal Steiner Tree Exact

Service ID: `graph-terminal-steiner-tree-exact`. USD 1.00 per job.

Find a minimum-weight connected edge subset spanning specified terminals in a bounded positive undirected graph, permitting Steiner vertices. Off-diagonal zero graph/cost entries denote absent edges; all matrix indices are zero-based.  Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=graph-terminal-steiner-tree-exact) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          3
        ],
        [
          1,
          0,
          1
        ],
        [
          3,
          1,
          0
        ]
      ],
      "terminals": [
        0,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/edges": [
    [
      0,
      1
    ],
    [
      1,
      2
    ]
  ],
  "/records/0/weight": 2,
  "/records/0/usedVertices": [
    0,
    1,
    2
  ]
}
```

## Weighted Maximum Coverage Cardinality

Service ID: `weighted-maximum-coverage-cardinality`. USD 1.00 per job.

Select at most a declared number of supplied sets to maximize covered element weight, retaining selected sets and uncovered elements. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=weighted-maximum-coverage-cardinality) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sets": [
        [
          0,
          1
        ],
        [
          1,
          2
        ]
      ],
      "weights": [
        1,
        2,
        4
      ],
      "maximumSets": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/selected": [
    1
  ],
  "/records/0/covered": [
    1,
    2
  ],
  "/records/0/uncovered": [
    0
  ],
  "/records/0/weight": 6
}
```

## Quadratic Binary Knapsack Exact

Service ID: `quadratic-binary-knapsack-exact`. USD 1.00 per job.

Maximize declared linear item benefits plus pairwise interactions under an integer capacity through exact subset enumeration. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=quadratic-binary-knapsack-exact) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        1,
        1
      ],
      "linear": [
        1,
        1
      ],
      "interaction": [
        [
          0,
          3
        ],
        [
          3,
          0
        ]
      ],
      "capacity": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/selected": [
    0,
    1
  ],
  "/records/0/value": 5,
  "/records/0/weight": 2
}
```

## Multiresource Zero One Knapsack

Service ID: `multiresource-zero-one-knapsack`. USD 1.00 per job.

Maximize additive item value under several independent exact integer resource budgets with a bounded exhaustive witness. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=multiresource-zero-one-knapsack) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "requirements": [
        [
          2,
          1
        ],
        [
          1,
          2
        ],
        [
          1,
          1
        ]
      ],
      "values": [
        3,
        4,
        2
      ],
      "budgets": [
        2,
        3
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/selected": [
    1,
    2
  ],
  "/records/0/value": 6,
  "/records/0/used": [
    2,
    3
  ]
}
```

## Identical Parallel Machine Makespan

Service ID: `identical-parallel-machine-makespan`. USD 1.00 per job.

Find a minimum makespan assignment of bounded positive-duration jobs to interchangeable machines using exhaustive symmetry-pruned assignments. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=identical-parallel-machine-makespan) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "duration": [
        3,
        2,
        2
      ],
      "machines": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/assignment": [
    0,
    1,
    1
  ],
  "/records/0/loads": [
    3,
    4
  ],
  "/records/0/makespan": 4
}
```

## Jobshop Operation Order Optimum

Service ID: `jobshop-operation-order-optimum`. USD 1.00 per job.

Find an optimal nonpreemptive job-shop makespan for bounded ordered operation routes by exhaustive feasible priority sequences with earliest-start placement. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=jobshop-operation-order-optimum) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "machine": [
        [
          0,
          1
        ],
        [
          1,
          0
        ]
      ],
      "duration": [
        [
          2,
          1
        ],
        [
          2,
          1
        ]
      ],
      "machines": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/start": [
    [
      0,
      2
    ],
    [
      0,
      2
    ]
  ],
  "/records/0/completion": [
    [
      2,
      3
    ],
    [
      2,
      3
    ]
  ],
  "/records/0/makespan": 3
}
```

## Maximum Weight Noncrossing Matching

Service ID: `maximum-weight-noncrossing-matching`. USD 1.00 per job.

Find a maximum-weight noncrossing matching on ordered boundary vertices, allowing unmatched vertices and retaining deterministic nested pairs. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=maximum-weight-noncrossing-matching) · [Technical reference](https://docs.scipy.org/doc/scipy/tutorial/optimize.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "weights": [
        [
          0,
          1,
          0,
          2
        ],
        [
          1,
          0,
          3,
          0
        ],
        [
          0,
          3,
          0,
          1
        ],
        [
          2,
          0,
          1,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/pairs": [
    [
      0,
      3
    ],
    [
      1,
      2
    ]
  ],
  "/records/0/weight": 5
}
```

## Confluent Hermite Derivative Interpolant

Service ID: `confluent-hermite-derivative-interpolant`. USD 1.00 per job.

Construct a polynomial satisfying supplied value/derivative constraints at repeated nodes, then evaluate it at explicit query locations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=confluent-hermite-derivative-interpolant) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "nodes": [
        0,
        1
      ],
      "derivatives": [
        [
          0,
          0
        ],
        [
          1,
          2
        ]
      ],
      "queries": [
        0.5
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coefficients": [
    0,
    0,
    1,
    0
  ],
  "/records/0/values": [
    0.25
  ]
}
```

## Ascending Polynomial Composition

Service ID: `ascending-polynomial-composition`. USD 1.00 per job.

Compose two finite ascending-power polynomials with an explicit degree/output-work bound, returning the full composed coefficient vector. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ascending-polynomial-composition) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "outer": [
        1,
        2,
        1
      ],
      "inner": [
        1,
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coefficients": [
    4,
    4,
    1
  ],
  "/records/0/degree": 2
}
```

## Bezier Control Polygon Subdivision

Service ID: `bezier-control-polygon-subdivision`. USD 1.00 per job.

Subdivide a supplied Cartesian Bezier control polygon at an interior parameter using de Casteljau construction, preserving both endpoint control polygons. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bezier-control-polygon-subdivision) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "control": [
        [
          0,
          0
        ],
        [
          1,
          2
        ],
        [
          2,
          0
        ]
      ],
      "parameter": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/left": [
    [
      0,
      0
    ],
    [
      0.5,
      1
    ],
    [
      1,
      1
    ]
  ],
  "/records/0/right": [
    [
      1,
      1
    ],
    [
      1.5,
      1
    ],
    [
      2,
      0
    ]
  ],
  "/records/0/join": [
    1,
    1
  ]
}
```

## Rational Bezier Homogeneous Evaluation

Service ID: `rational-bezier-homogeneous-evaluation`. USD 1.00 per job.

Evaluate a positive-weight rational Cartesian Bezier curve and its tangent by homogeneous de Casteljau differentiation. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rational-bezier-homogeneous-evaluation) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "control": [
        [
          0,
          0
        ],
        [
          2,
          0
        ]
      ],
      "weights": [
        1,
        1
      ],
      "parameter": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/point": [
    1,
    0
  ],
  "/records/0/tangent": [
    2,
    0
  ],
  "/records/0/homogeneousWeight": 1
}
```

## Bspline Single Knot Insertion

Service ID: `bspline-single-knot-insertion`. USD 1.00 per job.

Insert one interior knot into a supplied open B-spline control polygon, preserving the represented curve and recording the refined knot/control arrays. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bspline-single-knot-insertion) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.insert_knot.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "degree": 1,
      "knots": [
        0,
        0,
        1,
        1
      ],
      "control": [
        [
          0,
          0
        ],
        [
          2,
          0
        ]
      ],
      "knot": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/knots": [
    0,
    0,
    0.5,
    1,
    1
  ],
  "/records/0/control": [
    [
      0,
      0
    ],
    [
      1,
      0
    ],
    [
      2,
      0
    ]
  ]
}
```

## Periodic Cubic Spline Interpolant

Service ID: `periodic-cubic-spline-interpolant`. USD 1.00 per job.

Construct a periodic cubic spline on a supplied nonuniform closed cycle and evaluate in-cycle queries with value/derivative continuity. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=periodic-cubic-spline-interpolant) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "knots": [
        0,
        1,
        2,
        3
      ],
      "values": [
        1,
        1,
        1,
        1
      ],
      "queries": [
        0.5,
        2.5
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/values": [
    1,
    1
  ],
  "/records/0/derivatives": [
    0,
    0
  ],
  "/records/0/secondDerivatives": [
    0,
    0,
    0
  ]
}
```

## Tensor Chebyshev Value Gradient

Service ID: `tensor-chebyshev-value-gradient`. USD 1.00 per job.

Evaluate a rectangular bivariate first-kind Chebyshev series and both analytic partial derivatives within its declared unit square. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=tensor-chebyshev-value-gradient) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "coefficients": [
        [
          1,
          2
        ],
        [
          3,
          0
        ]
      ],
      "x": 0.5,
      "y": 0.25
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/value": 3,
  "/records/0/gradient": [
    3,
    2
  ]
}
```

## Legendre Elliptic First Second Integrals

Service ID: `legendre-elliptic-first-second-integrals`. USD 1.00 per job.

Evaluate real incomplete Legendre elliptic F and E integrals over a bounded amplitude with adaptive Richardson evidence from fixed paired Simpson grids. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=legendre-elliptic-first-second-integrals) · [Technical reference](https://dlmf.nist.gov/19.2)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "parameter": 0,
      "amplitudeRad": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/first": 1,
  "/records/0/second": 1,
  "/records/0/firstErrorEstimate": 0,
  "/records/0/secondErrorEstimate": 0
}
```

## Airy Real Function And Derivatives

Service ID: `airy-real-function-and-derivatives`. USD 1.00 per job.

Evaluate real Ai/Bi and their first derivatives by the defining Airy differential-equation power series on a bounded real interval. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=airy-real-function-and-derivatives) · [Technical reference](https://dlmf.nist.gov/9.2)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/ai": 0.3550280538878172,
  "/records/0/bi": 0.6149266274460007,
  "/records/0/aiPrime": -0.2588194037928068,
  "/records/0/biPrime": 0.4482883573538264
}
```

## Dawson Scaled Gaussian Integral

Service ID: `dawson-scaled-gaussian-integral`. USD 1.00 per job.

Evaluate Dawson F(x) through a bounded non-overflowing integral representation and return its differential-equation derivative. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dawson-scaled-gaussian-integral) · [Technical reference](https://dlmf.nist.gov/7.2)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/value": 0,
  "/records/0/derivative": 1,
  "/records/0/quadratureDifference": 0
}
```

## Entire Exponential Integral Ein

Service ID: `entire-exponential-integral-ein`. USD 1.00 per job.

Evaluate Ein(x)=integral(1-exp(-t))/t by its convergent entire series, preserving its removable derivative singularity at zero. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=entire-exponential-integral-ein) · [Technical reference](https://dlmf.nist.gov/6.2)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/value": 0,
  "/records/0/derivative": 1,
  "/records/0/terms": 1
}
```

## Classical Orthogonal Polynomial Table

Service ID: `classical-orthogonal-polynomial-table`. USD 1.00 per job.

Evaluate caller-selected Legendre, physicists Hermite or ordinary Laguerre polynomial tables and derivatives through a bounded degree using each defining recurrence. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=classical-orthogonal-polynomial-table) · [Technical reference](https://dlmf.nist.gov/18.9)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "family": "legendre",
      "degree": 2,
      "x": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/values": [
    1,
    0.5,
    -0.125
  ],
  "/records/0/derivatives": [
    0,
    1,
    1.5
  ]
}
```

## Positive Polygamma Derivative Profile

Service ID: `positive-polygamma-derivative-profile`. USD 1.00 per job.

Evaluate trigamma and tetragamma from convergent positive-domain sums with asymptotic tails, retaining their recurrence check residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=positive-polygamma-derivative-profile) · [Technical reference](https://dlmf.nist.gov/5.15)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/trigamma": 1.6449340668482264,
  "/records/0/tetragamma": -2.4041138063191885,
  "/records/0/recurrenceResidual": 0
}
```

## Riemann Zeta Positive Euler Maclaurin

Service ID: `riemann-zeta-positive-euler-maclaurin`. USD 1.00 per job.

Evaluate real zeta(s) for s>1 with Euler-Maclaurin tail terms and separately expose the tail contribution. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=riemann-zeta-positive-euler-maclaurin) · [Technical reference](https://dlmf.nist.gov/25.11)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "s": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/value": 1.6449340668482264
}
```

## Real Dilogarithm With Identity Check

Service ID: `real-dilogarithm-with-identity-check`. USD 1.00 per job.

Evaluate Li2(x) on a bounded real interval by convergent series and reflection, retaining its derivative and reflection-identity residual where defined. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=real-dilogarithm-with-identity-check) · [Technical reference](https://dlmf.nist.gov/25.12)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/value": 0.5822405264650126,
  "/records/0/derivative": 1.3862943611198906,
  "/records/0/reflectionResidual": 0
}
```

## Gauss Hypergeometric Series Profile

Service ID: `gauss-hypergeometric-series-profile`. USD 1.00 per job.

Evaluate real 2F1(a,b;c;z) and its z derivative by bounded convergent series with an explicit last-term convergence finding. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=gauss-hypergeometric-series-profile) · [Technical reference](https://dlmf.nist.gov/15.2)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": 1,
      "b": 1,
      "c": 1,
      "z": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/value": 2,
  "/records/0/derivative": 4,
  "/records/0/converged": true
}
```

## Struve Zero One Series

Service ID: `struve-zero-one-series`. USD 1.00 per job.

Evaluate the distinct inhomogeneous Struve H0/H1 functions and H0 derivative through their bounded real convergent power series. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=struve-zero-one-series) · [Technical reference](https://dlmf.nist.gov/11.2)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "x": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/h0": 0,
  "/records/0/h1": 0,
  "/records/0/h0Prime": 0.6366197723675814
}
```

## Complex Pivoted Linear System

Service ID: `complex-pivoted-linear-system`. USD 1.00 per job.

Solve bounded dense complex linear equations by complex partial pivoting and return a complex solution plus residual norm. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=complex-pivoted-linear-system) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "real": [
        [
          1,
          0
        ],
        [
          0,
          1
        ]
      ],
      "imag": [
        [
          0,
          0
        ],
        [
          0,
          0
        ]
      ],
      "rhsReal": [
        2,
        3
      ],
      "rhsImag": [
        4,
        5
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/solutionReal": [
    2,
    3
  ],
  "/records/0/solutionImag": [
    4,
    5
  ],
  "/records/0/residualNorm": 0
}
```

## Symmetric Definite Generalized Eigensystem

Service ID: `symmetric-definite-generalized-eigensystem`. USD 1.00 per job.

Solve a real symmetric generalized eigenproblem A*v=lambda*B*v with strictly positive-definite B and return B-orthonormal vectors and residuals. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=symmetric-definite-generalized-eigensystem) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.eigh.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          2,
          0
        ],
        [
          0,
          6
        ]
      ],
      "b": [
        [
          1,
          0
        ],
        [
          0,
          2
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/eigenvalues": [
    2,
    3
  ],
  "/records/0/eigenvectors": [
    [
      1,
      0
    ],
    [
      0,
      0.7071067811865475
    ]
  ],
  "/records/0/maximumResidual": 0
}
```

## Rectangular Matrix Polar Decomposition

Service ID: `rectangular-matrix-polar-decomposition`. USD 1.00 per job.

Construct the full-column-rank rectangular polar decomposition A=Q*H with symmetric positive-definite H, preserving reconstruction and orthogonality residuals. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rectangular-matrix-polar-decomposition) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.polar.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "matrix": [
        [
          2,
          0
        ],
        [
          0,
          3
        ],
        [
          0,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/orthogonal": [
    [
      1,
      0
    ],
    [
      0,
      1
    ],
    [
      0,
      0
    ]
  ],
  "/records/0/stretch": [
    [
      2,
      0
    ],
    [
      0,
      3
    ]
  ],
  "/records/0/reconstructionResidual": 0,
  "/records/0/orthogonalityResidual": 0
}
```

## Positive Definite Matrix Logarithm

Service ID: `positive-definite-matrix-logarithm`. USD 1.00 per job.

Evaluate the real symmetric principal logarithm of a strictly positive-definite matrix and report exponential reconstruction residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=positive-definite-matrix-logarithm) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.logm.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "matrix": [
        [
          1,
          0
        ],
        [
          0,
          2.718281828459045
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/logarithm": [
    [
      0,
      0
    ],
    [
      0,
      1
    ]
  ],
  "/records/0/reconstructionResidual": 0
}
```

## Positive Definite Geometric Matrix Mean

Service ID: `positive-definite-geometric-matrix-mean`. USD 1.00 per job.

Compute the affine-invariant geometric mean A#B of two real positive-definite matrices and retain its Riccati identity residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=positive-definite-geometric-matrix-mean) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          1,
          0
        ],
        [
          0,
          4
        ]
      ],
      "b": [
        [
          9,
          0
        ],
        [
          0,
          1
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/mean": [
    [
      3,
      0
    ],
    [
      0,
      2
    ]
  ],
  "/records/0/riccatiResidual": 0
}
```

## Two Pair Vertex Disjoint Path Optimum

Service ID: `two-pair-vertex-disjoint-path-optimum`. USD 1.00 per job.

Find a minimum-cost pair of fully vertex-disjoint directed simple paths for two fixed terminal pairs through bounded exact path enumeration. Off-diagonal zero graph/cost entries denote absent edges; all matrix indices are zero-based.  Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-pair-vertex-disjoint-path-optimum) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cost": [
        [
          0,
          1,
          0,
          0
        ],
        [
          0,
          0,
          0,
          0
        ],
        [
          0,
          0,
          0,
          2
        ],
        [
          0,
          0,
          0,
          0
        ]
      ],
      "pairs": [
        [
          0,
          1
        ],
        [
          2,
          3
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/paths": [
    [
      0,
      1
    ],
    [
      2,
      3
    ]
  ],
  "/records/0/totalCost": 3,
  "/records/0/feasible": true
}
```

## Discrete Lyapunov Stationary Covariance

Service ID: `discrete-lyapunov-stationary-covariance`. USD 1.00 per job.

Solve P=A*P*A^T+Q for a supplied strict Frobenius contraction and nonnegative symmetric process covariance, retaining equation residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=discrete-lyapunov-stationary-covariance) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_discrete_lyapunov.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          0.5
        ]
      ],
      "q": [
        [
          3
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/covariance": [
    [
      4
    ]
  ],
  "/records/0/equationResidual": 0
}
```

## Finite Horizon Discrete Lqr

Service ID: `finite-horizon-discrete-lqr`. USD 1.00 per job.

Solve a bounded finite-horizon discrete linear-quadratic supplied-model problem by Riccati backward recursion and return time-varying gains and cost matrices. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-horizon-discrete-lqr) · [Technical reference](https://underactuated.mit.edu/lqr.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          1
        ]
      ],
      "b": [
        [
          1
        ]
      ],
      "q": [
        [
          1
        ]
      ],
      "r": [
        [
          1
        ]
      ],
      "terminal": [
        [
          1
        ]
      ],
      "horizon": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gains": [
    [
      [
        0.5
      ]
    ]
  ],
  "/records/0/costMatrices": [
    [
      [
        1.5
      ]
    ],
    [
      [
        1
      ]
    ]
  ]
}
```

## Discrete Algebraic Riccati Iteration

Service ID: `discrete-algebraic-riccati-iteration`. USD 1.00 per job.

Iterate the discrete algebraic Riccati map from a supplied nonnegative initial matrix with an explicit iteration/tolerance profile and convergence finding. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=discrete-algebraic-riccati-iteration) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_discrete_are.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          0
        ]
      ],
      "b": [
        [
          1
        ]
      ],
      "q": [
        [
          1
        ]
      ],
      "r": [
        [
          1
        ]
      ],
      "initial": [
        [
          0
        ]
      ],
      "tolerance": 1e-10,
      "maximumIterations": 100
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/solution": [
    [
      1
    ]
  ],
  "/records/0/gain": [
    [
      0
    ]
  ],
  "/records/0/converged": true,
  "/records/0/iterations": 2,
  "/records/0/residualNorm": 0
}
```

## Zero Order Hold State Discretization

Service ID: `zero-order-hold-state-discretization`. USD 1.00 per job.

Discretize a supplied continuous linear state/input model under a zero-order hold using a block exponential, preserving the input integral at singular A. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=zero-order-hold-state-discretization) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.cont2discrete.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          0
        ]
      ],
      "b": [
        [
          2
        ]
      ],
      "sampleS": 3
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/discreteA": [
    [
      1
    ]
  ],
  "/records/0/discreteB": [
    [
      6
    ]
  ]
}
```

## State Observability Initial Reconstruction

Service ID: `state-observability-initial-reconstruction`. USD 1.00 per job.

Reconstruct the least-squares initial state of a supplied discrete state model from aligned controls/outputs and report the fitted output trajectory. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=state-observability-initial-reconstruction) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          1
        ]
      ],
      "b": [
        [
          1
        ]
      ],
      "c": [
        [
          1
        ]
      ],
      "controls": [
        [
          1
        ],
        [
          1
        ]
      ],
      "outputs": [
        [
          2
        ],
        [
          3
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/initialState": [
    2
  ],
  "/records/0/finalState": [
    4
  ],
  "/records/0/predicted": [
    [
      2
    ],
    [
      3
    ]
  ],
  "/records/0/residualNorm": 0
}
```

## Single Input Ackermann Pole Placement

Service ID: `single-input-ackermann-pole-placement`. USD 1.00 per job.

Compute a single-input state-feedback gain for explicitly supplied real desired poles by Ackermann construction, rejecting an uncontrollable model. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=single-input-ackermann-pole-placement) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          0,
          1
        ],
        [
          0,
          0
        ]
      ],
      "b": [
        0,
        1
      ],
      "desiredPoles": [
        -2,
        -3
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gain": [
    6,
    5
  ],
  "/records/0/closedLoop": [
    [
      0,
      1
    ],
    [
      -6,
      -5
    ]
  ],
  "/records/0/desiredPolynomial": [
    6,
    5,
    1
  ]
}
```

## Routh Hurwitz Sign Table

Service ID: `routh-hurwitz-sign-table`. USD 1.00 per job.

Construct a nonsingular real Routh table from descending polynomial coefficients and count strict right-half-plane roots by first-column sign changes. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=routh-hurwitz-sign-table) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "coefficients": [
        1,
        6,
        11,
        6
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/firstColumn": [
    1,
    6,
    10,
    6
  ],
  "/records/0/rightHalfPlaneRoots": 0,
  "/records/0/strictlyStable": true
}
```

## Complex Polygon Winding Evidence

Service ID: `complex-polygon-winding-evidence`. USD 1.00 per job.

Compute the signed winding of an explicitly closed complex response polygon around a supplied reference and its minimum segment clearance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=complex-polygon-winding-evidence) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "real": [
        0,
        -1,
        -2,
        -1,
        0
      ],
      "imag": [
        0,
        1,
        0,
        -1,
        0
      ],
      "referenceRe": -1,
      "referenceIm": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/winding": 1,
  "/records/0/minimumClearance": 0.7071067811865476,
  "/records/0/angleSumRad": 6.283185307179586
}
```

## Finite Horizon Minimum Energy Transfer

Service ID: `finite-horizon-minimum-energy-transfer`. USD 1.00 per job.

Construct a minimum-squared-input transfer between two declared states over a bounded discrete horizon, retaining control sequence and endpoint residual. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-horizon-minimum-energy-transfer) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          1
        ]
      ],
      "b": [
        [
          1
        ]
      ],
      "initial": [
        0
      ],
      "target": [
        2
      ],
      "horizon": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/controls": [
    [
      1
    ],
    [
      1
    ]
  ],
  "/records/0/trajectory": [
    [
      0
    ],
    [
      1
    ],
    [
      2
    ]
  ],
  "/records/0/energy": 2,
  "/records/0/endpointResidual": 0
}
```

## Finite Alphabet Predictive Control Rehearsal

Service ID: `finite-alphabet-predictive-control-rehearsal`. USD 1.00 per job.

Enumerate bounded finite control sequences for a supplied linear model and quadratic state/input costs, returning only a deterministic mathematical scenario. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-alphabet-predictive-control-rehearsal) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "a": [
        [
          1
        ]
      ],
      "b": [
        [
          1
        ]
      ],
      "initial": [
        1
      ],
      "target": [
        0
      ],
      "alphabet": [
        [
          -1
        ],
        [
          0
        ],
        [
          1
        ]
      ],
      "horizon": 2,
      "stateWeight": 1,
      "inputWeight": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/controls": [
    [
      -1
    ],
    [
      0
    ]
  ],
  "/records/0/trajectory": [
    [
      1
    ],
    [
      0
    ],
    [
      0
    ]
  ],
  "/records/0/cost": 1
}
```

## Complex Frequency Group Delay Profile

Service ID: `complex-frequency-group-delay-profile`. USD 1.00 per job.

Unwrap a supplied nonzero complex frequency response on a strictly increasing angular-frequency grid and compute local secant group-delay estimates. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=complex-frequency-group-delay-profile) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "omega": [
        0,
        1,
        2
      ],
      "real": [
        1,
        1,
        1
      ],
      "imag": [
        0,
        0,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/unwrappedPhase": [
    0,
    0,
    0
  ],
  "/records/0/groupDelay": [
    0,
    0,
    0
  ]
}
```

## Max Plus Event State Replay

Service ID: `max-plus-event-state-replay`. USD 1.00 per job.

Replay a supplied finite max-plus event transition matrix with explicit absent edges and initial finite event times, retaining each state and selected predecessors. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=max-plus-event-state-replay) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "matrix": [
        [
          0,
          1
        ],
        [
          null,
          0
        ]
      ],
      "initial": [
        0,
        0
      ],
      "steps": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/states": [
    [
      1,
      0
    ],
    [
      1,
      0
    ]
  ],
  "/records/0/predecessors": [
    [
      1,
      1
    ],
    [
      0,
      1
    ]
  ]
}
```

## Integer Lattice Box Closest Point

Service ID: `integer-lattice-box-closest-point`. USD 1.00 per job.

Find the exact nearest lattice point to an integer target within a supplied bounded coefficient box, retaining an exact decimal squared-distance certificate. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=integer-lattice-box-closest-point) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "basis": [
        [
          2,
          0
        ],
        [
          0,
          2
        ]
      ],
      "target": [
        1,
        0
      ],
      "lower": [
        -1,
        -1
      ],
      "upper": [
        1,
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coefficients": [
    0,
    0
  ],
  "/records/0/point": [
    "0",
    "0"
  ],
  "/records/0/squaredDistance": "1"
}
```

## Nonnegative Matrix Multiplicative Update

Service ID: `nonnegative-matrix-multiplicative-update`. USD 1.00 per job.

Perform one Frobenius-loss nonnegative matrix factorization update with an explicit positive-denominator profile, retaining both factors and reconstruction loss. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=nonnegative-matrix-multiplicative-update) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "data": [
        [
          2
        ]
      ],
      "w": [
        [
          1
        ]
      ],
      "h": [
        [
          1
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/w": [
    [
      1
    ]
  ],
  "/records/0/h": [
    [
      2
    ]
  ],
  "/records/0/reconstruction": [
    [
      2
    ]
  ],
  "/records/0/squaredError": 0
}
```

## Canonical Correlation Covariance Profile

Service ID: `canonical-correlation-covariance-profile`. USD 1.00 per job.

Compute canonical correlations from supplied positive-definite marginal covariance blocks and their cross covariance using symmetric whitening. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=canonical-correlation-covariance-profile) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "xx": [
        [
          1
        ]
      ],
      "yy": [
        [
          1
        ]
      ],
      "xy": [
        [
          0.5
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/correlations": [
    0.5
  ],
  "/records/0/whitenedCross": [
    [
      0.5
    ]
  ],
  "/records/0/maximumCorrelation": 0.5
}
```

## Masked Matrix Completion Als Update

Service ID: `masked-matrix-completion-als-update`. USD 1.00 per job.

Perform one ridge-regularized alternating least-squares sweep over explicitly observed matrix entries, retaining completed values and observed loss. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=masked-matrix-completion-als-update) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "data": [
        [
          2
        ]
      ],
      "observed": [
        [
          true
        ]
      ],
      "w": [
        [
          1
        ]
      ],
      "h": [
        [
          1
        ]
      ],
      "ridge": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/w": [
    [
      1
    ]
  ],
  "/records/0/h": [
    [
      1
    ]
  ],
  "/records/0/completed": [
    [
      1
    ]
  ],
  "/records/0/observedSquaredError": 1,
  "/records/0/regularizer": 2
}
```

## Multinomial Logit Loss Gradient Hessian

Service ID: `multinomial-logit-loss-gradient-hessian`. USD 1.00 per job.

Evaluate stable multinomial cross-entropy, gradient and full Hessian from supplied logits and a normalized target distribution, preserving large logit differences without log-of-zero. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. No external device or account is accessed. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=multinomial-logit-loss-gradient-hessian) · [Technical reference](https://dlmf.nist.gov/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "logits": [
        0,
        0
      ],
      "target": [
        1,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/probabilities": [
    0.5,
    0.5
  ],
  "/records/0/loss": 0.6931471805599453,
  "/records/0/gradient": [
    -0.5,
    0.5
  ],
  "/records/0/hessian": [
    [
      0.25,
      -0.25
    ],
    [
      -0.25,
      0.25
    ]
  ]
}
```

## Two Tone Third Order Intercept Record

Service ID: `two-tone-third-order-intercept-record`. USD 9.00 per job.

Reconcile equal-tone fundamental and third-order intermodulation power observations across a supplied test sweep, retaining per-point input/output intercepts and spread. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /outputInterceptDbm/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-tone-third-order-intercept-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputDbm": [
        0,
        1
      ],
      "outputDbm": [
        10,
        11
      ],
      "thirdOrderDbm": [
        -10,
        -7
      ],
      "reportedValue": 20,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/outputInterceptDbm": [
    20,
    20
  ],
  "/records/0/inputInterceptDbm": [
    10,
    10
  ],
  "/records/0/interceptSpreadDb": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/outputInterceptDbm/0",
  "/records/0/comparisonAvailable": true
}
```

## Swept Gain Compression Crossing Record

Service ID: `swept-gain-compression-crossing-record`. USD 9.00 per job.

Locate a supplied gain-compression crossing relative to an explicitly declared small-signal gain, retaining bracket endpoints and interpolated input/output levels. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /inputCrossingDbm using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=swept-gain-compression-crossing-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputDbm": [
        0,
        1,
        2
      ],
      "outputDbm": [
        10,
        10.5,
        10.5
      ],
      "referenceGainDb": 10,
      "compressionDb": 1,
      "reportedValue": 1.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/inputCrossingDbm": 1.5,
  "/records/0/outputCrossingDbm": 10.5,
  "/records/0/bracketIndices": [
    1,
    2
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/inputCrossingDbm",
  "/records/0/comparisonAvailable": true
}
```

## Mixer Conversion Image Ledger Record

Service ID: `mixer-conversion-image-ledger-record`. USD 9.00 per job.

Reconcile declared high-side or low-side downconversion observations into RF/image frequencies, conversion gains and summed desired output power. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /rfHz/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mixer-conversion-image-ledger-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "loHz": 100,
      "ifHz": [
        10,
        20
      ],
      "sideband": [
        1,
        -1
      ],
      "inputW": [
        2,
        4
      ],
      "outputW": [
        1,
        1
      ],
      "reportedValue": 110,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/rfHz": [
    110,
    80
  ],
  "/records/0/imageHz": [
    90,
    120
  ],
  "/records/0/conversionGain": [
    0.5,
    0.25
  ],
  "/records/0/totalOutputW": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/rfHz/0",
  "/records/0/comparisonAvailable": true
}
```

## Receiver Hot Cold Y Factor Record

Service ID: `receiver-hot-cold-y-factor-record`. USD 9.00 per job.

Separate equivalent receiver noise temperature and linear power gain-bandwidth from two supplied matched thermal-source observations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /yFactor using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=receiver-hot-cold-y-factor-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "hotK": 300,
      "coldK": 100,
      "hotPower": 5,
      "coldPower": 3,
      "reportedValue": 1.6666666666666667,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/yFactor": 1.6666666666666667,
  "/records/0/receiverK": 200,
  "/records/0/powerPerK": 0.01,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/yFactor",
  "/records/0/comparisonAvailable": true
}
```

## Spectrum Noise Equivalent Bandwidth Record

Service ID: `spectrum-noise-equivalent-bandwidth-record`. USD 9.00 per job.

Reconcile already linear-power-averaged analyzer noise observations with supplied resolution-bandwidth shape factors and input loss. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /inputWPerHz/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=spectrum-noise-equivalent-bandwidth-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "powerW": [
        2,
        4
      ],
      "resolutionHz": [
        1,
        2
      ],
      "shapeFactor": [
        2,
        2
      ],
      "inputLossLinear": 2,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/inputWPerHz": [
    2,
    2
  ],
  "/records/0/meanWPerHz": 2,
  "/records/0/relativeSpread": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/inputWPerHz/0",
  "/records/0/comparisonAvailable": true
}
```

## Phase Noise Integrated Jitter Record

Service ID: `phase-noise-integrated-jitter-record`. USD 9.00 per job.

Integrate supplied single-sideband phase-noise samples in linear power using the stated piecewise-linear spectrum model and convert phase variance to carrier timing jitter. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /phaseVarianceRad2 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=phase-noise-integrated-jitter-record) · [Technical reference](https://www.analog.com/media/en/technical-documentation/data-sheets/AD9508.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "offsetHz": [
        1,
        2,
        3
      ],
      "ssbDbcPerHz": [
        -10,
        -10,
        -10
      ],
      "carrierHz": 1,
      "reportedValue": 0.4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/phaseVarianceRad2": 0.4,
  "/records/0/phaseRmsRad": 0.6324555320336759,
  "/records/0/timeRmsS": 0.10065842420897407,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/phaseVarianceRad2",
  "/records/0/comparisonAvailable": true
}
```

## Oscillator Quadratic Time Error Record

Service ID: `oscillator-quadratic-time-error-record`. USD 9.00 per job.

Resolve constant phase-time offset, fractional frequency offset and linear frequency drift from three equally spaced clock time-error observations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /offsetS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=oscillator-quadratic-time-error-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timeErrorS": [
        1,
        4,
        9
      ],
      "spacingS": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/offsetS": 1,
  "/records/0/fractionalFrequency": 2,
  "/records/0/frequencyDriftPerS": 2,
  "/records/0/predictedNextErrorS": 16,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/offsetS",
  "/records/0/comparisonAvailable": true
}
```

## Fractional N Divider Dwell Record

Service ID: `fractional-n-divider-dwell-record`. USD 9.00 per job.

Reconcile exact integer divider dwell counts into average division ratio, declared PFD output frequency and ratio quantization variance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /meanDivision using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fractional-n-divider-dwell-record) · [Technical reference](https://www.analog.com/en/resources/analog-dialogue/articles/pll-synthesizers.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "dividers": [
        2,
        3
      ],
      "counts": [
        3,
        1
      ],
      "pfdHz": 4,
      "reportedValue": 2.25,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/meanDivision": 2.25,
  "/records/0/outputHz": 9,
  "/records/0/divisionVariance": 0.1875,
  "/records/0/totalDwell": 4,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/meanDivision",
  "/records/0/comparisonAvailable": true
}
```

## Resonator Half Power Bracket Record

Service ID: `resonator-half-power-bracket-record`. USD 9.00 per job.

Reconcile an observed power-response sweep into linearly bracketed half-power crossings and loaded Q without extrapolating missing sides. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /peakHz using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=resonator-half-power-bracket-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "frequencyHz": [
        1,
        2,
        3,
        4,
        5
      ],
      "power": [
        0,
        1,
        2,
        1,
        0
      ],
      "reportedValue": 3,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/peakHz": 3,
  "/records/0/lowerHalfHz": 2,
  "/records/0/upperHalfHz": 4,
  "/records/0/loadedQ": 1.5,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/peakHz",
  "/records/0/comparisonAvailable": true
}
```

## Resonator Amplitude Ringdown Q Record

Service ID: `resonator-amplitude-ringdown-q-record`. USD 9.00 per job.

Fit the logarithm of a supplied positive decaying amplitude envelope and reconcile amplitude time constant with loaded resonator Q. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /timeConstantS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=resonator-amplitude-ringdown-q-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "amplitude": [
        1,
        0.36787944117144233,
        0.1353352832366127
      ],
      "frequencyHz": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/timeConstantS": 1,
  "/records/0/loadedQ": 3.141592653589793,
  "/records/0/logRmsResidual": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/timeConstantS",
  "/records/0/comparisonAvailable": true
}
```

## Vna Periodic Time Gate Record

Service ID: `vna-periodic-time-gate-record`. USD 9.00 per job.

Apply an explicitly supplied finite time gate to the periodic impulse response of uniformly spaced complex transfer samples and retain removed time-domain energy. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /gatedReal/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=vna-periodic-time-gate-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "real": [
        1,
        1
      ],
      "imag": [
        0,
        0
      ],
      "gate": [
        true,
        false
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gatedReal": [
    1,
    1
  ],
  "/records/0/gatedImag": [
    0,
    0
  ],
  "/records/0/removedEnergy": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/gatedReal/0",
  "/records/0/comparisonAvailable": true
}
```

## Rf Unknown Phase Mismatch Envelope Record

Service ID: `rf-unknown-phase-mismatch-envelope-record`. USD 9.00 per job.

Reconcile measured reflection magnitudes into the exact delivered-power factor envelope over unknown relative phase and retain its dB bounds. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /minimumFactor using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rf-unknown-phase-mismatch-envelope-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sourceMagnitude": 0.5,
      "loadMagnitude": 0.5,
      "reportedValue": 0.36,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/minimumFactor": 0.36,
  "/records/0/maximumFactor": 1,
  "/records/0/minimumDb": -4.436974992327127,
  "/records/0/maximumDb": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/minimumFactor",
  "/records/0/comparisonAvailable": true
}
```

## Antenna Gain Substitution Geometry Record

Service ID: `antenna-gain-substitution-geometry-record`. USD 9.00 per job.

Reconcile a reference/test antenna substitution with explicitly supplied distances and cable losses into gain ratio and each geometry correction. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /gainRatio using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=antenna-gain-substitution-geometry-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceReceivedW": 1,
      "testReceivedW": 2,
      "referenceDistanceM": 1,
      "testDistanceM": 2,
      "referenceCableLoss": 1,
      "testCableLoss": 2,
      "referenceGain": 3,
      "reportedValue": 16,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gainRatio": 16,
  "/records/0/testGain": 48,
  "/records/0/distanceCorrection": 4,
  "/records/0/cableCorrection": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/gainRatio",
  "/records/0/comparisonAvailable": true
}
```

## Array Pattern Complex Observation Record

Service ID: `array-pattern-complex-observation-record`. USD 9.00 per job.

Reconcile a declared one-dimensional point-source array with supplied complex excitations and measured normalized directional powers. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /predictedNormalized/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=array-pattern-complex-observation-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "positionM": [
        0,
        0.5
      ],
      "weightRe": [
        1,
        1
      ],
      "weightIm": [
        0,
        0
      ],
      "directionCosine": [
        0,
        1
      ],
      "wavelengthM": 1,
      "measuredNormalized": [
        1,
        0
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictedNormalized": [
    1,
    0
  ],
  "/records/0/residual": [
    0,
    0
  ],
  "/records/0/rmsResidual": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/predictedNormalized/0",
  "/records/0/comparisonAvailable": true
}
```

## Coax Echo Roundtrip Loss Record

Service ID: `coax-echo-roundtrip-loss-record`. USD 9.00 per job.

Reconcile same-polarity successive echo magnitudes with explicit end reflection magnitudes into round-trip attenuation and per-length loss. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /roundTripAmplitude using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=coax-echo-roundtrip-loss-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "echoV": [
        4,
        2,
        1
      ],
      "sourceReflection": 0.5,
      "loadReflection": 1,
      "lengthM": 1,
      "reportedValue": 0.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/roundTripAmplitude": 0.5,
  "/records/0/propagationAmplitude": 1,
  "/records/0/lossDbPerM": 0,
  "/records/0/ratioSpread": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/roundTripAmplitude",
  "/records/0/comparisonAvailable": true
}
```

## Directional Coupler Port Power Record

Service ID: `directional-coupler-port-power-record`. USD 9.00 per job.

Reconcile four supplied forward-excitation port powers into insertion, coupling, isolation and directivity while retaining net unaccounted power. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /insertionDb using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=directional-coupler-port-power-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputW": 10,
      "throughW": 8,
      "coupledW": 1,
      "isolatedW": 0.1,
      "reportedValue": 0.9691001300805642,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/insertionDb": 0.9691001300805642,
  "/records/0/couplingDb": 10,
  "/records/0/isolationDb": 20,
  "/records/0/directivityDb": 10,
  "/records/0/unaccountedW": 0.9,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/insertionDb",
  "/records/0/comparisonAvailable": true
}
```

## Multiport Scattering Passivity Record

Service ID: `multiport-scattering-passivity-record`. USD 9.00 per job.

Assess the largest singular-value power gain of a supplied complex scattering matrix and retain each single-port outgoing-power sum. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /maximumPowerGain using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=multiport-scattering-passivity-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "real": [
        [
          0,
          0.5
        ],
        [
          0.5,
          0
        ]
      ],
      "imag": [
        [
          0,
          0
        ],
        [
          0,
          0
        ]
      ],
      "reportedValue": 0.25,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/maximumPowerGain": 0.25,
  "/records/0/singlePortGain": [
    0.25,
    0.25
  ],
  "/records/0/passiveSuppliedModel": true,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/maximumPowerGain",
  "/records/0/comparisonAvailable": true
}
```

## Impedance Fixture Open Short Record

Service ID: `impedance-fixture-open-short-record`. USD 9.00 per job.

Correct one measured complex DUT impedance using explicitly supplied series-short and parallel-open fixture error terms. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /corrected/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=impedance-fixture-open-short-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "measured": [
        3,
        0
      ],
      "short": [
        1,
        0
      ],
      "openAdmittance": [
        0.25,
        0
      ],
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/corrected": [
    4,
    0
  ],
  "/records/0/seriesRemoved": [
    2,
    0
  ],
  "/records/0/parallelRemoved": [
    0.25,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/corrected/0",
  "/records/0/comparisonAvailable": true
}
```

## Scope Channel Deskew Differential Record

Service ID: `scope-channel-deskew-differential-record`. USD 9.00 per job.

Reconcile a declared channel skew by bounded linear interpolation of one supplied waveform onto the other channel timestamps, retaining overlap and differential RMS. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /timesS/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=scope-channel-deskew-differential-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "firstV": [
        0,
        1,
        2
      ],
      "secondV": [
        0,
        1,
        2
      ],
      "secondSkewS": 0,
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/timesS": [
    0,
    1,
    2
  ],
  "/records/0/differentialV": [
    0,
    0,
    0
  ],
  "/records/0/rmsV": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/timesS/0",
  "/records/0/comparisonAvailable": true
}
```

## Sampling Aperture Jitter Budget Record

Service ID: `sampling-aperture-jitter-budget-record`. USD 9.00 per job.

Reconcile uncorrelated aperture timing jitter with an explicitly supplied multisine RMS spectrum into derivative-weighted noise and a signal-to-jitter ratio. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /signalRmsV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sampling-aperture-jitter-budget-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "toneRmsV": [
        1,
        1
      ],
      "frequencyHz": [
        1,
        2
      ],
      "jitterS": 0.01,
      "reportedValue": 1.4142135623730951,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/signalRmsV": 1.4142135623730951,
  "/records/0/jitterNoiseRmsV": 0.14049629462081453,
  "/records/0/snrDb": 20.05700254611732,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/signalRmsV",
  "/records/0/comparisonAvailable": true
}
```

## Adc Arcsine Histogram Linearity Record

Service ID: `adc-arcsine-histogram-linearity-record`. USD 9.00 per job.

Reconcile a declared sinusoidal ADC code histogram with normalized transition levels using exact arcsine-bin probabilities rather than a uniform-stimulus assumption. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /expectedFraction/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=adc-arcsine-histogram-linearity-record) · [Technical reference](https://www.analog.com/en/resources/technical-articles/histogram-testing-determines-dnl-and-inl-errors.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "edges": [
        -1,
        0,
        1
      ],
      "counts": [
        5,
        5
      ],
      "reportedValue": 0.5,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/expectedFraction": [
    0.5,
    0.5
  ],
  "/records/0/dnl": [
    0,
    0
  ],
  "/records/0/inl": [
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/expectedFraction/0",
  "/records/0/comparisonAvailable": true
}
```

## Time Interleaved Adc Spur Record

Service ID: `time-interleaved-adc-spur-record`. USD 9.00 per job.

Construct an explicitly supplied interleaved-channel sine observation from channel gain/offset/timing errors and reconcile selected DFT-bin amplitudes against measured bins. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /predictedAmplitude/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=time-interleaved-adc-spur-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "channelGain": [
        1,
        1
      ],
      "channelOffsetV": [
        0,
        0
      ],
      "channelSkewSamples": [
        0,
        0
      ],
      "cyclesPerSample": 0.25,
      "samples": 4,
      "bins": [
        1
      ],
      "measuredAmplitude": [
        1
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictedAmplitude": [
    1
  ],
  "/records/0/amplitudeResidual": [
    0
  ],
  "/records/0/rmsSampleErrorV": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/predictedAmplitude/0",
  "/records/0/comparisonAvailable": true
}
```

## Dac Settling Last Exit Record

Service ID: `dac-settling-last-exit-record`. USD 9.00 per job.

Locate the earliest measured sample after which an entire supplied response remains within an explicitly declared final-value band, retaining unresolved acquisition windows. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /settlingS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dac-settling-last-exit-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2,
        3
      ],
      "volts": [
        0,
        1.2,
        1.05,
        1
      ],
      "finalV": 1,
      "toleranceV": 0.1,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/settled": true,
  "/records/0/settlingS": 2,
  "/records/0/lastOutsideIndex": 1,
  "/records/0/maximumLateErrorV": 0.05,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/settlingS",
  "/records/0/comparisonAvailable": true
}
```

## Isolator Paired Edge Delay Record

Service ID: `isolator-paired-edge-delay-record`. USD 9.00 per job.

Reconcile paired rising/falling input/output edge timestamps into polarity-specific propagation delays, pulse-width distortion and measured spread. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /risingDelayS/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=isolator-paired-edge-delay-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inputRiseS": [
        0,
        10
      ],
      "outputRiseS": [
        1,
        11
      ],
      "inputFallS": [
        4,
        14
      ],
      "outputFallS": [
        6,
        16
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/risingDelayS": [
    1,
    1
  ],
  "/records/0/fallingDelayS": [
    2,
    2
  ],
  "/records/0/pulseDistortionS": [
    1,
    1
  ],
  "/records/0/meanDistortionS": 1,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/risingDelayS/0",
  "/records/0/comparisonAvailable": true
}
```

## Clock High Low Jitter Covariance Record

Service ID: `clock-high-low-jitter-covariance-record`. USD 9.00 per job.

Reconcile paired positive high/low clock durations into period variance, component variances and their covariance identity. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /periodMeanS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=clock-high-low-jitter-covariance-record) · [Technical reference](https://www.dspguide.com/ch9/2.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "highS": [
        1,
        2,
        3
      ],
      "lowS": [
        3,
        2,
        1
      ],
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/periodMeanS": 4,
  "/records/0/periodVarianceS2": 0,
  "/records/0/highVarianceS2": 1,
  "/records/0/lowVarianceS2": 1,
  "/records/0/covarianceS2": -1,
  "/records/0/varianceClosureS2": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/periodMeanS",
  "/records/0/comparisonAvailable": true
}
```

## Crystal Resonator Motional Parameter Record

Service ID: `crystal-resonator-motional-parameter-record`. USD 9.00 per job.

Resolve an ideal Butterworth-Van Dyke resonator motional branch from supplied series/parallel frequencies, static capacitance and motional resistance. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /motionalF using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=crystal-resonator-motional-parameter-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "seriesHz": 1,
      "parallelHz": 1.4142135623730951,
      "staticF": 1,
      "motionalOhm": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/motionalF": 1,
  "/records/0/motionalH": 0.025330295910584444,
  "/records/0/quality": 0.15915494309189535,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/motionalF",
  "/records/0/comparisonAvailable": true
}
```

## Depletion Capacitance Doping Profile Record

Service ID: `depletion-capacitance-doping-profile-record`. USD 9.00 per job.

Reconcile a positive reverse-bias junction capacitance sweep into interval depletion widths and apparent doping from inverse-capacitance-squared slopes. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /depletionM/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=depletion-capacitance-doping-profile-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "reverseV": [
        0,
        1,
        2
      ],
      "capacitanceF": [
        1,
        0.7071067811865475,
        0.5773502691896258
      ],
      "areaM2": 1,
      "permittivityFPerM": 1,
      "chargeC": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/depletionM": [
    1,
    1.4142135623730951,
    1.7320508075688772
  ],
  "/records/0/apparentDensity": [
    2,
    2
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/depletionM/0",
  "/records/0/comparisonAvailable": true
}
```

## Mos Flatband Charge Ledger Record

Service ID: `mos-flatband-charge-ledger-record`. USD 9.00 per job.

Reconcile an oxide flatband voltage shift with declared work-function difference, oxide capacitance, area and signed elementary charge into equivalent sheet charge. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /totalChargeC using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mos-flatband-charge-ledger-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "flatbandV": -1,
      "workFunctionV": 1,
      "oxideF": 2,
      "areaM2": 4,
      "chargeC": 1,
      "reportedValue": 4,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/totalChargeC": 4,
  "/records/0/sheetCPerM2": 1,
  "/records/0/equivalentChargesPerM2": 1,
  "/records/0/oxideVolts": 2,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/totalChargeC",
  "/records/0/comparisonAvailable": true
}
```

## Bjt Output Early Voltage Fit Record

Service ID: `bjt-output-early-voltage-fit-record`. USD 9.00 per job.

Fit positive forward-active collector-current observations against collector-emitter voltage and retain apparent Early voltage plus current residuals. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /earlyV using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bjt-output-early-voltage-fit-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "collectorV": [
        1,
        2,
        3
      ],
      "collectorA": [
        2,
        3,
        4
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/earlyV": 1,
  "/records/0/interceptA": 1,
  "/records/0/outputOhm": 1,
  "/records/0/residualA": [
    0,
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/earlyV",
  "/records/0/comparisonAvailable": true
}
```

## Charge Pumping Interface Trap Fit Record

Service ID: `charge-pumping-interface-trap-fit-record`. USD 9.00 per job.

Separate frequency-proportional charge-pumping current and frequency-independent leakage, then reconcile equivalent active interface trap density. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /leakageA using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=charge-pumping-interface-trap-fit-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "frequencyHz": [
        1,
        2,
        3
      ],
      "currentA": [
        3,
        5,
        7
      ],
      "areaM2": 2,
      "chargeC": 1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/leakageA": 1,
  "/records/0/chargePerCycleC": 2,
  "/records/0/equivalentTrapDensityPerM2": 1,
  "/records/0/rmsResidualA": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/leakageA",
  "/records/0/comparisonAvailable": true
}
```

## Fet Transconductance Local Threshold Record

Service ID: `fet-transconductance-local-threshold-record`. USD 9.00 per job.

Reconcile a monotone supplied gate/current sweep into interval transconductance and local linear tangent threshold estimates at each interval midpoint. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /transconductanceS/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fet-transconductance-local-threshold-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gateV": [
        1,
        2,
        3
      ],
      "drainA": [
        1,
        4,
        9
      ],
      "reportedValue": 3,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/transconductanceS": [
    3,
    5
  ],
  "/records/0/midpointV": [
    1.5,
    2.5
  ],
  "/records/0/tangentThresholdV": [
    0.6666666666666666,
    1.2
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/transconductanceS/0",
  "/records/0/comparisonAvailable": true
}
```

## Thermal Impedance Power Step Record

Service ID: `thermal-impedance-power-step-record`. USD 9.00 per job.

Reconcile a declared multi-exponential transient thermal impedance with supplied power-step history and observed junction-temperature rises at explicit times. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /predictedRiseK/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=thermal-impedance-power-step-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "stepTimesS": [
        0,
        1
      ],
      "stepW": [
        2,
        -2
      ],
      "thermalKPerW": [
        1
      ],
      "timeConstantsS": [
        1
      ],
      "observationS": [
        0,
        1,
        2
      ],
      "observedRiseK": [
        0,
        1.2642411176571153,
        0.46508831586965926
      ],
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictedRiseK": [
    0,
    1.2642411176571153,
    0.46508831586965926
  ],
  "/records/0/residualK": [
    0,
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/predictedRiseK/0",
  "/records/0/comparisonAvailable": true
}
```

## Capacitor Two Mode Absorption Current Fit Record

Service ID: `capacitor-two-mode-absorption-current-fit-record`. USD 9.00 per job.

Separate two supplied known-time-constant absorption modes and a constant leakage current from three current observations, retaining mode amplitudes and fit residuals. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /leakageA using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=capacitor-two-mode-absorption-current-fit-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "timesS": [
        0,
        1,
        2
      ],
      "currentA": [
        4,
        1.8710941655794975,
        1.2889862053619596
      ],
      "tau1S": 1,
      "tau2S": 0.5,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/leakageA": 1,
  "/records/0/modeA": [
    2,
    1
  ],
  "/records/0/residualA": [
    0,
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/leakageA",
  "/records/0/comparisonAvailable": true
}
```

## Dielectric Debye Semicircle Residual Record

Service ID: `dielectric-debye-semicircle-residual-record`. USD 9.00 per job.

Reconcile supplied complex permittivity observations against a declared single-Debye relaxation semicircle, retaining center/radius and per-observation radial deviations. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /center using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dielectric-debye-semicircle-residual-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "epsilonStatic": 5,
      "epsilonInfinity": 1,
      "real": [
        5,
        3,
        1
      ],
      "lossPositive": [
        0,
        2,
        0
      ],
      "reportedValue": 3,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/center": 3,
  "/records/0/radius": 2,
  "/records/0/radialResidual": [
    0,
    0,
    0
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/center",
  "/records/0/comparisonAvailable": true
}
```

## Arbitrary Angle Strain Rosette Record

Service ID: `arbitrary-angle-strain-rosette-record`. USD 9.00 per job.

Resolve three strain-gauge readings at supplied nondegenerate in-plane angles into the symmetric strain tensor, principal strains and principal direction. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /strainX using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=arbitrary-angle-strain-rosette-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "angleRad": [
        0,
        0.7853981633974483,
        1.5707963267948966
      ],
      "strain": [
        1,
        0.5,
        0
      ],
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/strainX": 1,
  "/records/0/strainY": 0,
  "/records/0/engineeringShear": 0,
  "/records/0/principal": [
    1,
    0
  ],
  "/records/0/principalAngleRad": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/strainX",
  "/records/0/comparisonAvailable": true
}
```

## Thermistor Three Point Steinhart Hart Record

Service ID: `thermistor-three-point-steinhart-hart-record`. USD 9.00 per job.

Fit three-parameter Steinhart-Hart coefficients from three positive resistance/Kelvin references and evaluate supplied query resistances without extrapolation. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /coefficients/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=thermistor-three-point-steinhart-hart-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "resistanceOhm": [
        1,
        2.718281828459045,
        7.38905609893065
      ],
      "temperatureK": [
        1000,
        500,
        333.3333333333333
      ],
      "queryOhm": [
        1.6487212707001282
      ],
      "reportedValue": 0.001,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coefficients": [
    0.001,
    0.001,
    0
  ],
  "/records/0/queryK": [
    666.6666666666666
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/coefficients/0",
  "/records/0/comparisonAvailable": true
}
```

## Rtd Callendar Van Dusen Inversion Record

Service ID: `rtd-callendar-van-dusen-inversion-record`. USD 9.00 per job.

Reconcile a caller-supplied Callendar-Van Dusen RTD characteristic with measured four-wire resistances over an explicit temperature bracket with A positive and B/C nonpositive, ensuring monotonicity analytically. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /temperatureC/0 using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rtd-callendar-van-dusen-inversion-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "r0Ohm": 100,
      "aPerC": 0.01,
      "bPerC2": 0,
      "cPerC4": 0,
      "minimumC": 0,
      "maximumC": 100,
      "measuredOhm": [
        100,
        150,
        200
      ],
      "reportedValue": 0,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/temperatureC": [
    0,
    50,
    100
  ],
  "/records/0/residualOhm": [
    0,
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/temperatureC/0",
  "/records/0/comparisonAvailable": true
}
```

## Differential Capacitive Position Parasitic Record

Service ID: `differential-capacitive-position-parasitic-record`. USD 9.00 per job.

Resolve an ideal differential parallel-plate displacement sensor after separately supplied per-side parasitic subtraction and retain common-mode capacitance closure. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /positionM using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=differential-capacitive-position-parasitic-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "firstF": 3,
      "secondF": 1.5,
      "parasiticFirstF": 1,
      "parasiticSecondF": 0.5,
      "gapM": 1,
      "centerF": 1.3333333333333333,
      "reportedValue": 0.3333333333333333,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/positionM": 0.3333333333333333,
  "/records/0/normalizedDifference": 0.3333333333333333,
  "/records/0/predictedCommonF": 3,
  "/records/0/commonResidualF": 0,
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/positionM",
  "/records/0/comparisonAvailable": true
}
```

## Acoustic Opposed Transit Medium Record

Service ID: `acoustic-opposed-transit-medium-record`. USD 9.00 per job.

Resolve two opposed acoustic transit observations along a supplied path into intrinsic sound speed and medium velocity projection, retaining transit reconstruction residuals. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /soundMPerS using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=acoustic-opposed-transit-medium-record) · [Technical reference](https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pathM": 3,
      "downstreamS": 1,
      "upstreamS": 3,
      "projectionCosine": 1,
      "reportedValue": 2,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/soundMPerS": 2,
  "/records/0/mediumMPerS": 1,
  "/records/0/reconstructedS": [
    1,
    3
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/soundMPerS",
  "/records/0/comparisonAvailable": true
}
```

## Otdr Backscatter Segment Loss Record

Service ID: `otdr-backscatter-segment-loss-record`. USD 9.00 per job.

Reconcile a declared optical backscatter segment under explicit double-pass propagation into one-way attenuation and separate supplied splice jumps. Declared ideal or supplied-record model only; no physical inspection, live control, certification or professional approval. Nonzero model inputs have magnitude from 1e-12 through 1e9; zero remains permitted only where the specific semantic model permits it. reportedValue and absoluteTolerance may use smaller finite magnitudes. Explicit matrix pivot/spectral conditioning floor is 1e-12 of the stated scale; symmetric eigensystem stopping is 1e-14 of scale. Matrix and enumeration bounds are input work profiles. Floating arithmetic uses finite double precision and twelve-significant-digit presentation; integral quantities must remain exactly representable. Compare supplied reportedValue with the model result at record JSON pointer /oneWayDbPerM using supplied absoluteTolerance; a strictly larger absolute residual creates a finding. An unavailable target creates a finding with null residual. The comparison has no hidden epsilon. Aggregate enumeration estimates must not exceed 10000000 elementary work units per request. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=otdr-backscatter-segment-loss-record) · [Technical reference](https://www.emva.org/standards-technology/emva-1288/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "distanceM": [
        0,
        1,
        2
      ],
      "backscatterDb": [
        0,
        -2,
        -4
      ],
      "spliceBeforeDb": 0,
      "spliceAfterDb": -1,
      "reportedValue": 1,
      "absoluteTolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/oneWayDbPerM": 1,
  "/records/0/oneWaySpliceDb": 0.5,
  "/records/0/fitResidualDb": [
    0,
    0,
    0
  ],
  "/records/0/reportedResidual": 0,
  "/records/0/comparisonTolerance": 1e-8,
  "/records/0/comparisonTarget": "/oneWayDbPerM",
  "/records/0/comparisonAvailable": true
}
```

## Two Peg Level Collimation Field Record

Service ID: `two-peg-level-collimation-field-record`. USD 9.00 per job.

Reduce a two-peg collimation test using equal midpoint sights and unequal near-end sights; output is rod-reading slope error per distance. No instrument adjustment or accuracy-class assignment. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-peg-level-collimation-field-record) · [Technical reference](https://www.itftennis.com/media/14104/2025-technical-booklet.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "nearA": 2,
      "nearB": 1,
      "middleA": 2,
      "middleB": 1.1,
      "nearDistanceA": 1,
      "nearDistanceB": 11,
      "observedValue": -0.01,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": -0.01,
  "/records/0/observedValue": -0.01,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Reciprocal Trigonometric Height Pair Record

Service ID: `reciprocal-trigonometric-height-pair-record`. USD 9.00 per job.

Average reciprocal trigonometric height differences in a common length unit with separately supplied instrument and target heights. Equal path conditions are assumed; no refraction or datum certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Curvature/refraction cancellation assumes simultaneous symmetrical reciprocal paths with comparable ground/atmosphere; distances share the same meteorological convention. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=reciprocal-trigonometric-height-pair-record) · [Technical reference](https://kdl.kogistate.gov.ng/wp-content/uploads/2023/08/Engineering-Surveying.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "forwardSlope": 2,
      "forwardZenithDegrees": 60,
      "reverseSlope": 2,
      "reverseZenithDegrees": 120,
      "forwardInstrumentHeight": 1,
      "forwardTargetHeight": 1,
      "reverseInstrumentHeight": 1,
      "reverseTargetHeight": 1,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Total Station Zenith Face Index Record

Service ID: `total-station-zenith-face-index-record`. USD 9.00 per job.

Reconcile the vertical-circle index from a paired face-I/face-II zenith observation in degrees. Full-circle opposite-face convention only; no automatic total-station calibration. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=total-station-zenith-face-index-record) · [Technical reference](https://www.meteo.be/uploads/media/666abc1b7991a/user-manual-flm5-rev0.pdf?v20250724-1333=)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "faceOneDegrees": 80.01,
      "faceTwoDegrees": 280.01,
      "observedValue": 0.01,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.01,
  "/records/0/observedValue": 0.01,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Horizontal Circle Set Wrap Reduction Record

Service ID: `horizontal-circle-set-wrap-reduction-record`. USD 9.00 per job.

Reduce a repeated horizontal angle set with circular averaging across circle zero. Back/fore readings share face convention; no traverse adjustment or orientation certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. observedValue must use the same 0 to 360 degree representative as calculatedValue; discrepancy is ordinary absolute subtraction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=horizontal-circle-set-wrap-reduction-record) · [Technical reference](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.circmean.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "rounds": [
        {
          "backsight": 170,
          "foresight": -170
        },
        {
          "backsight": 0,
          "foresight": 20
        }
      ],
      "observedValue": 20,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 20,
  "/records/0/observedValue": 20,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Edm Baseline Additive Scale Calibration Record

Service ID: `edm-baseline-additive-scale-calibration-record`. USD 9.00 per job.

Fit additive and proportional EDM discrepancy across supplied reference baselines, then report predicted discrepancy at a supplied test distance. No traceability or calibration certificate is issued. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=edm-baseline-additive-scale-calibration-record) · [Technical reference](https://medjil0.lb.landgate.wa.gov.au/calibrationguide/read_manual/edmi_calibration_manual.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "baselines": [
        {
          "certified": 1,
          "measured": 1.1
        },
        {
          "certified": 2,
          "measured": 2.2
        },
        {
          "certified": 3,
          "measured": 3.3
        }
      ],
      "testDistance": 10,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Steel Tape Sag Tension Temperature Record

Service ID: `steel-tape-sag-tension-temperature-record`. USD 9.00 per job.

Reconcile a level steel tape length with thermal, elastic pull and parabolic uniform-span sag corrections. Common force/length units and small sag are required; no field distance certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=steel-tape-sag-tension-temperature-record) · [Technical reference](https://archive.nptel.ac.in/content/storage2/courses/105107122/modules/module3/htmlpage/24.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "measuredLength": 10,
      "referenceTemperature": 20,
      "fieldTemperature": 30,
      "expansionPerDegree": 0.00001,
      "fieldTension": 10,
      "referenceTension": 10,
      "area": 1,
      "youngModulus": 100,
      "weightPerLength": 0,
      "unsupportedSpan": 10,
      "observedValue": 10.001,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 10.001,
  "/records/0/observedValue": 10.001,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Inclined Stadia Vertical Staff Reduction Record

Service ID: `inclined-stadia-vertical-staff-reduction-record`. USD 9.00 per job.

Reduce inclined stadia observations on a vertical staff into target-ground elevation difference. Assumes a declared multiplying/additive instrument model; no target height inference or survey approval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=inclined-stadia-vertical-staff-reduction-record) · [Technical reference](https://archive.nptel.ac.in/content/storage2/courses/105107122/modules/module7/html/115.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "upperWire": 2,
      "lowerWire": 1,
      "centralWire": 1.5,
      "verticalAngleDegrees": 30,
      "multiplyingConstant": 100,
      "additiveConstant": 0,
      "instrumentHeight": 1.5,
      "observedValue": 43.30127018922193,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 43.30127018922193,
  "/records/0/observedValue": 43.30127018922193,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Level Staff Piecewise Scale Temperature Record

Service ID: `level-staff-piecewise-scale-temperature-record`. USD 9.00 per job.

Apply interpolated staff graduation correction followed by a declared thermal scale adjustment in the reading unit. No extrapolation, calibration authority or instrument change. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=level-staff-piecewise-scale-temperature-record) · [Technical reference](https://www.ngs.noaa.gov/PUBS_LIB/TMNOSNGS34.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "reading": 1.5,
      "temperature": 20,
      "referenceTemperature": 20,
      "expansionPerDegree": 0,
      "calibration": [
        {
          "reading": 1,
          "correction": 0.01
        },
        {
          "reading": 2,
          "correction": 0.03
        }
      ],
      "observedValue": 1.52,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1.52,
  "/records/0/observedValue": 1.52,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Curvature Refraction Intervisibility Clearance Record

Service ID: `curvature-refraction-intervisibility-clearance-record`. USD 9.00 per job.

Compare minimum supplied-profile sight clearance after the parabolic Earth-curvature/refraction bulge approximation. No terrain sampling completeness, visibility guarantee or radio propagation model. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=curvature-refraction-intervisibility-clearance-record) · [Technical reference](https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.526-16-202511-I!!PDF-E.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lineLength": 2,
      "startHeight": 1,
      "endHeight": 1,
      "earthRadius": 10,
      "refractionCoefficient": 0,
      "terrain": [
        {
          "station": 1,
          "height": 0
        }
      ],
      "observedValue": 0.95,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.95,
  "/records/0/observedValue": 0.95,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Prismoidal Earthwork Section Volume Record

Service ID: `prismoidal-earthwork-section-volume-record`. USD 9.00 per job.

Reconcile a prismoidal earthwork volume from endpoint and true midpoint cross-sectional areas. Common area/length units; no terrain model, shrink/swell factor or quantity certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=prismoidal-earthwork-section-volume-record) · [Technical reference](https://www.aust.edu/lab_manuals/CE/CE%20208.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "length": 6,
      "startArea": 1,
      "midArea": 4,
      "endArea": 9,
      "observedValue": 26,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 26,
  "/records/0/observedValue": 26,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Borehole Minimum Curvature Trajectory Record

Service ID: `borehole-minimum-curvature-trajectory-record`. USD 9.00 per job.

Reconcile vertical-depth change along a supplied borehole survey by the minimum-curvature method. Inclination is from downward vertical; no drilling control, positional accuracy or trajectory certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=borehole-minimum-curvature-trajectory-record) · [Technical reference](https://github.com/Zabamund/wellpathpy/blob/master/wellpathpy/mincurve.py)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "stations": [
        {
          "measuredDepth": 0,
          "inclinationDegrees": 0,
          "azimuthDegrees": 0
        },
        {
          "measuredDepth": 10,
          "inclinationDegrees": 0,
          "azimuthDegrees": 0
        }
      ],
      "observedValue": 10,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 10,
  "/records/0/observedValue": 10,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Stream Midsection Current Meter Discharge Record

Service ID: `stream-midsection-current-meter-discharge-record`. USD 9.00 per job.

Reduce a current-meter cross section by the USGS midsection method with explicit zero-depth bank endpoints and signed mean vertical velocities. Output is volume per time; no discharge measurement certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=stream-midsection-current-meter-discharge-record) · [Technical reference](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap10_15.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "verticals": [
        {
          "station": 0,
          "depth": 0,
          "velocity": 0
        },
        {
          "station": 1,
          "depth": 1,
          "velocity": 2
        },
        {
          "station": 2,
          "depth": 0,
          "velocity": 0
        }
      ],
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Moving Bed Loop Adcp Discharge Correction Record

Service ID: `moving-bed-loop-adcp-discharge-correction-record`. USD 9.00 per job.

Apply a supplied stationary-bed loop estimate to bottom-track-biased ADCP discharge using a uniform fractional moving-bed correction. No compass calibration, raw acoustic processing or deployment approval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=moving-bed-loop-adcp-discharge-correction-record) · [Technical reference](https://water.usgs.gov/water-resources/memos/memo.php?id=648)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "uncorrectedDischarge": 90,
      "boatLoopSeconds": 10,
      "upstreamClosureDistance": 1,
      "meanMeasuredWaterSpeed": 0.9,
      "observedValue": 100,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 100,
  "/records/0/observedValue": 100,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Contracted Rectangular Weir Field Discharge Record

Service ID: `contracted-rectangular-weir-field-discharge-record`. USD 9.00 per job.

Reconcile a fully contracted free rectangular sharp-crested Francis weir with two end contractions and head at most one-third of crest length. Coefficient must match the supplied coherent units. Approach and installation conditions must be supplied independently; no submergence, calibration or actual structure validation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=contracted-rectangular-weir-field-discharge-record) · [Technical reference](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap07_09.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "crestLength": 4,
      "head": 1,
      "endContractions": 2,
      "coefficient": 1,
      "observedValue": 3.8,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 3.8,
  "/records/0/observedValue": 3.8,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Submerged Weir Villemonte Discharge Record

Service ID: `submerged-weir-villemonte-discharge-record`. USD 9.00 per job.

Apply the explicitly approximate Villemonte submerged-weir reduction to a supplied free-flow discharge. No free-flow coefficient selection or suitability for a particular structure is inferred. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. This source-bound rectangular profile fixes weirExponent at1.5. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=submerged-weir-villemonte-discharge-record) · [Technical reference](https://www.hec.usace.army.mil/confluence/ressimguides/how-to-articles/how-to-add-real-time-gate-operation-capability-to-a-ressim-model)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "freeDischarge": 2,
      "upstreamHead": 1,
      "downstreamHead": 0,
      "weirExponent": 1.5,
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Tipping Bucket Dead Time Rain Intensity Record

Service ID: `tipping-bucket-dead-time-rain-intensity-record`. USD 9.00 per job.

Correct a tipping-bucket interval intensity in mm/h under a declared nonparalyzable per-tip dead-time model. No splash/undercatch correction or observed weather validation. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=tipping-bucket-dead-time-rain-intensity-record) · [Technical reference](https://hess.copernicus.org/articles/15/679/2011/hess-15-679-2011.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "tips": 10,
      "bucketDepthMm": 0.2,
      "seconds": 100,
      "deadSecondsPerTip": 1,
      "observedValue": 80,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 80,
  "/records/0/observedValue": 80,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Weighing Rain Gauge Reset Evaporation Record

Service ID: `weighing-rain-gauge-reset-evaporation-record`. USD 9.00 per job.

Reconstruct water-equivalent precipitation depth in mm from weighing-gauge mass increments, explicit reset removal additions and evaporation replacements. Assumes water density 1 kg/L; no automatic reset detection. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=weighing-rain-gauge-reset-evaporation-record) · [Technical reference](https://amt.copernicus.org/articles/19/4943/2026/amt-19-4943-2026.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "readingsKg": [
        10,
        11,
        2
      ],
      "resetAddedKg": [
        0,
        10
      ],
      "evaporationKg": [
        0,
        0
      ],
      "collectorAreaM2": 1,
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Double Mass Rainfall Slope Break Record

Service ID: `double-mass-rainfall-slope-break-record`. USD 9.00 per job.

Compare post-break to pre-break double-mass accumulation slopes at an explicitly supplied breakpoint. No automated changepoint, station homogeneity conclusion or rainfall correction is performed. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=double-mass-rainfall-slope-break-record) · [Technical reference](https://www.usgs.gov/publications/double-mass-curves-a-section-fitting-curves-cyclic-data)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "reference": [
        1,
        2,
        1,
        2
      ],
      "target": [
        2,
        4,
        1,
        2
      ],
      "breakAfter": 2,
      "observedValue": 0.5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.5,
  "/records/0/observedValue": 0.5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Snow Core Layer Water Equivalent Record

Service ID: `snow-core-layer-water-equivalent-record`. USD 9.00 per job.

Reconcile layered snow-core water equivalent in mm from measured layer thickness and bulk density. Excludes ice lenses outside supplied layers, spatial representativeness and runoff forecasting. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Water density is conventionally1000kg/m³. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=snow-core-layer-water-equivalent-record) · [Technical reference](https://raw.githubusercontent.com/peckhams/topoflow36/master/topoflow/components/snow_base.py)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "layers": [
        {
          "depthM": 0.1,
          "densityKgM3": 100
        },
        {
          "depthM": 0.2,
          "densityKgM3": 200
        }
      ],
      "observedValue": 50,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 50,
  "/records/0/observedValue": 50,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Section Sediment Flux Nozzle Sampling Reconciliation

Service ID: `section-sediment-flux-nozzle-sampling-reconciliation`. USD 9.00 per job.

Reconcile a contiguous set of supplied rectangular section strips with matched depth-mean flow and bottle evidence. Correct each dry filter gain by its supplied blank; combine concentration with each represented strip discharge into sediment mass flux and conserved discharge-weighted concentration. Independently calculate bottle-volume/nozzle-area/time intake velocity versus supplied ambient velocity and flag ratios outside the supplied tolerance. Offsets/depth metres, velocity m/s, volume mL and mass mg give concentration kg/m3 and flux kg/s. Strips and samples must represent the same supplied section/time. No correction of sampling bias, particle-size certification, full velocity-profile inference or approval of a field sampling method. Observed value is section sediment mass flux. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=section-sediment-flux-nozzle-sampling-reconciliation) · [Technical reference](https://webstatic.niwa.co.nz/library/NIWAsts6.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "strips": [
        {
          "leftOffset": 0,
          "rightOffset": 1,
          "depth": 2,
          "ambientVelocity": 1,
          "driedFilterMg": 11,
          "filterTareMg": 8,
          "blankGainMg": 2,
          "sampleVolumeMl": 1,
          "samplingSeconds": 1,
          "nozzleAreaM2": 0.000001
        },
        {
          "leftOffset": 1,
          "rightOffset": 3,
          "depth": 1,
          "ambientVelocity": 2,
          "driedFilterMg": 16,
          "filterTareMg": 8,
          "blankGainMg": 2,
          "sampleVolumeMl": 2,
          "samplingSeconds": 1,
          "nozzleAreaM2": 0.000001
        }
      ],
      "isokineticRatioTolerance": 0.1,
      "observedValue": 14,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 14,
  "/records/0/concentrations": [
    1,
    3
  ],
  "/records/0/waterDischarges": [
    2,
    4
  ],
  "/records/0/sedimentFluxes": [
    2,
    12
  ],
  "/records/0/intakeVelocities": [
    1,
    2
  ],
  "/records/0/isokineticRatios": [
    1,
    1
  ],
  "/records/0/correctedSedimentMassesMg": [
    1,
    6
  ],
  "/records/0/representedArea": 4,
  "/records/0/totalBlankMassMg": 4,
  "/records/0/totalWaterDischarge": 6,
  "/records/0/sedimentMassFlux": 14,
  "/records/0/dischargeWeightedConcentration": 2.3333333333333335,
  "/records/0/fluxBalanceResidual": 0,
  "/records/0/isokineticOutlierCount": 0,
  "/records/0/observedValue": 14,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Bedload Sampler Traverse Mass Rate Record

Service ID: `bedload-sampler-traverse-mass-rate-record`. USD 9.00 per job.

Expand a supplied bedload sampler traverse to dry mass per time using represented widths, nozzle width and declared efficiency. No sampler efficiency calibration or transport formula is inferred. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bedload-sampler-traverse-mass-rate-record) · [Technical reference](https://water.usgs.gov/water-basics_glossary.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "verticals": [
        {
          "width": 2,
          "dryMass": 3,
          "seconds": 1,
          "nozzleWidth": 1,
          "efficiency": 0.5
        }
      ],
      "observedValue": 12,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 12,
  "/records/0/observedValue": 12,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Ice Covered Vertical Current Area Record

Service ID: `ice-covered-vertical-current-area-record`. USD 9.00 per job.

Reduce under-ice subsection discharge from measured ice draft, slush and signed effective mean velocity. No open-water velocity conversion, ice strength or passage safety determination. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ice-covered-vertical-current-area-record) · [Technical reference](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap02_04.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "verticals": [
        {
          "width": 2,
          "totalDepth": 3,
          "iceDraft": 0.5,
          "slushDepth": 0.5,
          "meanVelocity": 2
        }
      ],
      "observedValue": 8,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 8,
  "/records/0/observedValue": 8,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Shifted Rating Hydrograph Volume Duration Report

Service ID: `shifted-rating-hydrograph-volume-duration-report`. USD 9.00 per job.

Reconcile a supplied stage hydrograph under a fixed shifted power rating Q=C*max(stage-zero-shift,0)^n. Exactly integrate the declared nonlinear rating over linearly interpolated stages, split zero crossings, retain point-flow residuals and interval/cumulative volumes, and measure zero/low-flow durations. Reject heads above the supplied rating range. Coherent supplied time/flow units; no rating fit, time-varying shift, extrapolation approval, flood forecast or live flow claim. Observed value is total volume. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=shifted-rating-hydrograph-volume-duration-report) · [Technical reference](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap10_17.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "zeroFlowStage": 0,
      "shift": 0,
      "coefficient": 2,
      "exponent": 2,
      "maximumEffectiveHead": 3,
      "lowFlowThreshold": 2,
      "points": [
        {
          "time": 0,
          "stage": -1,
          "observedDischarge": 0
        },
        {
          "time": 2,
          "stage": 1,
          "observedDischarge": 2
        },
        {
          "time": 4,
          "stage": 3,
          "observedDischarge": 18
        }
      ],
      "observedValue": 18,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 18,
  "/records/0/flows": [
    0,
    2,
    18
  ],
  "/records/0/flowResiduals": [
    0,
    0,
    0
  ],
  "/records/0/flowRootMeanSquareResidual": 0,
  "/records/0/intervalVolumes": [
    0.6666666666666666,
    17.333333333333332
  ],
  "/records/0/cumulativeVolumes": [
    0,
    0.6666666666666666,
    18
  ],
  "/records/0/totalVolume": 18,
  "/records/0/zeroFlowDuration": 1,
  "/records/0/positiveFlowDuration": 3,
  "/records/0/lowFlowDuration": 2,
  "/records/0/observedValue": 18,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Bank Erosion Pin Retreat Area Record

Service ID: `bank-erosion-pin-retreat-area-record`. USD 9.00 per job.

Reconcile signed bank-retreat volume from exposed-pin changes and declared bank-height/represented-length panels. Burial is negative retreat; no pin movement diagnosis or reach-scale sediment-budget certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bank-erosion-pin-retreat-area-record) · [Technical reference](https://www.usgs.gov/publications/bank-erosion-mass-wasting-water-clarity-bathymetry-and-a-sediment-budget-along-dam)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pins": [
        {
          "representedLength": 2,
          "initialExposed": 1,
          "finalExposed": 1.5,
          "bankHeight": 3
        }
      ],
      "observedValue": 3,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 3,
  "/records/0/observedValue": 3,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Pulse Tracer Dilution Streamflow Record

Service ID: `pulse-tracer-dilution-streamflow-record`. USD 9.00 per job.

Reduce a complete pulse-tracer concentration-time curve to ideal steady streamflow by mass conservation. Assumes full recovery, mixing and compatible units; no chemical release or real sampling validation. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pulse-tracer-dilution-streamflow-record) · [Technical reference](https://water.usgs.gov/osw/pubs/disp/dispersion.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "injectedMass": 4,
      "times": [
        0,
        1,
        2
      ],
      "concentrations": [
        0,
        2,
        0
      ],
      "background": 0,
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Constant Tracer Injection Discharge Record

Service ID: `constant-tracer-injection-discharge-record`. USD 9.00 per job.

Reconcile upstream streamflow from a constant-injection dilution plateau including injection volume in the mixture balance. Complete steady mixing only; no tracer dispensing or environmental approval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=constant-tracer-injection-discharge-record) · [Technical reference](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap12_04.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "injectionRate": 1,
      "stockConcentration": 10,
      "backgroundConcentration": 0,
      "plateauConcentration": 2,
      "observedValue": 4,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 4,
  "/records/0/observedValue": 4,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Paired Cross Section Wet Bed Change Survey Report

Service ID: `paired-cross-section-wet-bed-change-survey-report`. USD 9.00 per job.

Reconcile raw paired bed-elevation transects on one supplied fixed vertical datum and identical chainage/offset alignment. Split piecewise-linear profiles at waterline and bed crossings to compute wet areas and gross submerged deposition/erosion separately. Retain each section balance and separate reach volumes with net water-capacity conservation. Longitudinal volumes use the declared average-end-area approximation between surveyed sections; above-water material and unsurveyed reach structure are excluded. Datum/alignment labels are compared, not independently verified or transformed. Coherent length units produce square/cubic units; no continuous3D accuracy, survey certification, density or sediment mass claim. Compare observedValue to net deposition volume with supplied absolute tolerance; equality passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=paired-cross-section-wet-bed-change-survey-report) · [Technical reference](https://www.hec.usace.army.mil/publications/ComputerProgramDocumentation/HEC-6_UsersManual_(CPD-6).pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "beforeDatum": "LOCAL_FIXED_VERTICAL",
      "afterDatum": "LOCAL_FIXED_VERTICAL",
      "beforeAlignment": "TRANSECT_GRID_A",
      "afterAlignment": "TRANSECT_GRID_A",
      "waterElevation": 0,
      "sections": [
        {
          "chainageBefore": 0,
          "chainageAfter": 0,
          "offsetsBefore": [
            0,
            2
          ],
          "offsetsAfter": [
            0,
            2
          ],
          "elevationsBefore": [
            -1,
            1
          ],
          "elevationsAfter": [
            1,
            -1
          ]
        },
        {
          "chainageBefore": 10,
          "chainageAfter": 10,
          "offsetsBefore": [
            0,
            2
          ],
          "offsetsAfter": [
            0,
            2
          ],
          "elevationsBefore": [
            -1,
            1
          ],
          "elevationsAfter": [
            1,
            -1
          ]
        }
      ],
      "observedValue": 0,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0,
  "/records/0/areasBefore": [
    0.5,
    0.5
  ],
  "/records/0/areasAfter": [
    0.5,
    0.5
  ],
  "/records/0/depositionAreas": [
    0.5,
    0.5
  ],
  "/records/0/erosionAreas": [
    0.5,
    0.5
  ],
  "/records/0/sectionBalanceResiduals": [
    0,
    0
  ],
  "/records/0/interiorCrossingCounts": [
    1,
    1
  ],
  "/records/0/depositionVolume": 5,
  "/records/0/erosionVolume": 5,
  "/records/0/netDepositionVolume": 0,
  "/records/0/waterCapacityBefore": 5,
  "/records/0/waterCapacityAfter": 5,
  "/records/0/waterCapacityLoss": 0,
  "/records/0/volumeBalanceResidual": 0,
  "/records/0/observedValue": 0,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Step Drawdown Two Coefficient Well Loss Record

Service ID: `step-drawdown-two-coefficient-well-loss-record`. USD 9.00 per job.

Reduce two stabilized well-test steps into BQ plus CQ squared loss and reconcile drawdown at a supplied test rate. No parameter uncertainty, interference correction or pumping approval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=step-drawdown-two-coefficient-well-loss-record) · [Technical reference](https://books.gw-project.org/an-introduction-to-hydraulic-testing-in-hydrogeology/chapter/performance-tests-specific-capacity-data-and-estimating-t/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "rateA": 1,
      "drawdownA": 3,
      "rateB": 2,
      "drawdownB": 8,
      "testRate": 3,
      "observedValue": 15,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 15,
  "/records/0/observedValue": 15,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Packer Lugeon Pressure Interval Record

Service ID: `packer-lugeon-pressure-interval-record`. USD 9.00 per job.

Normalize a supplied water-pressure packer interval to Lugeon units with explicit gauge elevation minus static water elevation and a subtracted line-loss correction. Linear pressure normalization only; no rock permeability classification or injection control. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=packer-lugeon-pressure-interval-record) · [Technical reference](https://books.gw-project.org/an-introduction-to-hydraulic-testing-in-hydrogeology/chapter/testing-methods-and-analyses/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "flowLitresMinute": 2,
      "testLengthMetres": 2,
      "gaugePressureBar": 10,
      "gaugeElevationAboveTestM": 0,
      "staticWaterElevationAboveTestM": 0,
      "lineLossBar": 0,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Borehole Spinner Zone Flow Increment Record

Service ID: `borehole-spinner-zone-flow-increment-record`. USD 9.00 per job.

Reconcile the signed zone contribution between calibrated spinner observations immediately above and below a borehole interval. Uniform circular flow area; no raw spinner transfer fit or fracture identification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=borehole-spinner-zone-flow-increment-record) · [Technical reference](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap02_04.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "upperPassVelocity": 3,
      "lowerPassVelocity": 1,
      "boreholeDiameter": 2,
      "spinnerCalibrationFactor": 1,
      "observedValue": 6.283185307179586,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 6.283185307179586,
  "/records/0/observedValue": 6.283185307179586,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Seepage Meter Flexible Bag Exchange Record

Service ID: `seepage-meter-flexible-bag-exchange-record`. USD 9.00 per job.

Reconcile signed seepage flux from a flexible-bag seepage-meter volume change after a supplied blank change. No bag resistance, lakebed disturbance correction or groundwater discharge certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=seepage-meter-flexible-bag-exchange-record) · [Technical reference](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2026WR043579?af=R)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "bagInitialVolume": 1,
      "bagFinalVolume": 3,
      "blankVolumeChange": 0.5,
      "domeArea": 2,
      "elapsed": 3,
      "observedValue": 0.25,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.25,
  "/records/0/observedValue": 0.25,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Green Ampt Event Hyetograph Infiltration Record

Service ID: `green-ampt-event-hyetograph-infiltration-record`. USD 9.00 per job.

Reconcile event infiltration through a piecewise-constant rainfall hyetograph using Green-Ampt ponding transitions and the implicit integrated capacity equation. Retain cumulative infiltration and immediately removed rainfall excess at each interval. No surface detention, inter-event drying, lateral flow or calibrated runoff forecast. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=green-ampt-event-hyetograph-infiltration-record) · [Technical reference](https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.5/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "conductivity": 1,
      "suctionMoistureProduct": 1,
      "initialInfiltration": 0,
      "rain": [
        {
          "duration": 1,
          "intensity": 0.5
        },
        {
          "duration": 1,
          "intensity": 0.5
        }
      ],
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/cumulativeInfiltration": [
    0.5,
    1
  ],
  "/records/0/cumulativeExcess": [
    0,
    0
  ],
  "/records/0/rainfallDepth": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Ccd Row Overscan Science Sum Record

Service ID: `ccd-row-overscan-science-sum-record`. USD 9.00 per job.

Reconcile a raw science-region ADU total after independent row-median overscan subtraction. No bias structure, dark, flat or gain correction is implied. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ccd-row-overscan-science-sum-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "science": [
        [
          10,
          12
        ],
        [
          20,
          22
        ]
      ],
      "overscan": [
        [
          2,
          2
        ],
        [
          4,
          4
        ]
      ],
      "observedValue": 52,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 52,
  "/records/0/observedValue": 52,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Bias Subtracted Master Dark Scaling Record

Service ID: `bias-subtracted-master-dark-scaling-record`. USD 9.00 per job.

Reconcile a science ADU sum after bias subtraction and exposure-scaled bias-free master dark. Identical detector temperature/configuration is assumed; no dark-current fitting or detector control. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bias-subtracted-master-dark-scaling-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "darkPixels": [
        3,
        5
      ],
      "biasPixels": [
        1,
        1
      ],
      "darkExposure": 2,
      "scienceExposure": 4,
      "sciencePixels": [
        10,
        20
      ],
      "observedValue": 16,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 16,
  "/records/0/observedValue": 16,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Normalized Flatfield Science Calibration Record

Service ID: `normalized-flatfield-science-calibration-record`. USD 9.00 per job.

Reconcile the flat-corrected science ADU sum using a mean-normalized strictly positive bias-free flat. No scattered-light, pixel area or illumination correction is inferred. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=normalized-flatfield-science-calibration-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "scienceBiasFree": [
        10,
        20
      ],
      "flatBiasFree": [
        1,
        3
      ],
      "observedValue": 33.333333333333336,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 33.333333333333336,
  "/records/0/observedValue": 33.333333333333336,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Quadratic Ccd Response Linearization Record

Service ID: `quadratic-ccd-response-linearization-record`. USD 9.00 per job.

Invert the declared monotone detector response raw = linear + coefficient times linear squared and reconcile total linearized signal. Stable positive root only; no empirical nonlinearity calibration. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=quadratic-ccd-response-linearization-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "rawSignals": [
        2,
        6
      ],
      "quadraticCoefficient": 1,
      "observedValue": 3,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 3,
  "/records/0/observedValue": 3,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Shutter Timing Illumination Ratio Record

Service ID: `shutter-timing-illumination-ratio-record`. USD 9.00 per job.

Reduce constant-lamp short/long exposure counts to a uniform additive shutter timing offset and reconcile effective science exposure in seconds. No spatial shutter map or hardware adjustment. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=shutter-timing-illumination-ratio-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "shortExposure": 1,
      "longExposure": 3,
      "shortCounts": 2,
      "longCounts": 4,
      "commandedScienceExposure": 5,
      "observedValue": 6,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 6,
  "/records/0/observedValue": 6,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Three Position Parabolic Focus Minimum Record

Service ID: `three-position-parabolic-focus-minimum-record`. USD 9.00 per job.

Reconcile the interpolated minimum of a convex squared stellar-width focus parabola from three ordered positions. No motor control, PSF model fit or focus guarantee. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=three-position-parabolic-focus-minimum-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "focusPositions": [
        -1,
        0,
        1
      ],
      "squaredWidths": [
        5,
        2,
        1
      ],
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Bidirectional Filter Focus Backlash Record

Service ID: `bidirectional-filter-focus-backlash-record`. USD 9.00 per job.

Cancel a common symmetric approach-direction offset when reconciling a filter focus displacement from matched forward/reverse focus determinations. No actuator backlash calibration or autofocus execution. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bidirectional-filter-focus-backlash-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceForward": 100,
      "referenceReverse": 104,
      "filterForward": 110,
      "filterReverse": 114,
      "observedValue": 10,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 10,
  "/records/0/observedValue": 10,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Photon Transfer Paired Flat Gain Record

Service ID: `photon-transfer-paired-flat-gain-record`. USD 9.00 per job.

Reconcile electrons-per-ADU gain from the slope of two paired-flat difference variances versus mean ADU. Assumes equal independent frames and linear shot-noise regime; no detector certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=photon-transfer-paired-flat-gain-record) · [Technical reference](https://msfc-ccd.readthedocs.io/en/latest/reports/gain.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "meanA": 10,
      "meanB": 20,
      "differenceVarianceA": 12,
      "differenceVarianceB": 22,
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Fringe Template Background Scale Record

Service ID: `fringe-template-background-scale-record`. USD 9.00 per job.

Fit an additive sky intercept plus a zero-mean fringe-template scale on supplied sky pixels and reconcile the correction at one template value. No object masking, fringe discovery or spectral sky model. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fringe-template-background-scale-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "scienceSky": [
        8,
        10,
        12
      ],
      "fringeTemplate": [
        -1,
        0,
        1
      ],
      "targetTemplateValue": 2,
      "observedValue": 4,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 4,
  "/records/0/observedValue": 4,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Inverse Variance Photometric Coadd Record

Service ID: `inverse-variance-photometric-coadd-record`. USD 9.00 per job.

Reconcile an inverse-variance coadded count rate from independently calibrated exposure counts and variances. Variance is per integrated count measurement; no image registration, clipping or correlated-noise correction. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=inverse-variance-photometric-coadd-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "exposures": [
        {
          "counts": 2,
          "seconds": 1,
          "variance": 1
        },
        {
          "counts": 8,
          "seconds": 2,
          "variance": 4
        }
      ],
      "observedValue": 3,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 3,
  "/records/0/observedValue": 3,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Ensemble Reference Differential Photometry Record

Service ID: `ensemble-reference-differential-photometry-record`. USD 9.00 per job.

Reconcile a target relative flux after weighted ensemble-reference transparency normalization to a declared baseline. Comparison stars are supplied and assumed stable; no variable-star classification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ensemble-reference-differential-photometry-record) · [Technical reference](https://ccdproc.readthedocs.io/en/latest/reduction_toolbox.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "targetFlux": 80,
      "baselineTargetFlux": 100,
      "references": [
        {
          "currentFlux": 50,
          "baselineFlux": 100,
          "weight": 1
        },
        {
          "currentFlux": 100,
          "baselineFlux": 200,
          "weight": 1
        }
      ],
      "observedValue": 1.6,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1.6,
  "/records/0/observedValue": 1.6,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Photometric Zero Colour Extinction Fit Record

Service ID: `photometric-zero-colour-extinction-fit-record`. USD 9.00 per job.

Fit one nightly magnitude zero point, first-order airmass extinction and colour term, then reconcile the target transformation. Three independent design columns required; no absolute standard-star validation. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=photometric-zero-colour-extinction-fit-record) · [Technical reference](https://classic.sdss.org/dr5/algorithms/jeg_photometric_eq_dr1.php)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "standards": [
        {
          "airmass": 1,
          "colour": 0,
          "instrumentMinusCatalog": 2
        },
        {
          "airmass": 2,
          "colour": 0,
          "instrumentMinusCatalog": 3
        },
        {
          "airmass": 1,
          "colour": 1,
          "instrumentMinusCatalog": 4
        }
      ],
      "targetAirmass": 2,
      "targetColour": 1,
      "observedValue": 5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 5,
  "/records/0/observedValue": 5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Sip Astrometric Pixel Distortion Record

Service ID: `sip-astrometric-pixel-distortion-record`. USD 9.00 per job.

Reconcile the forward SIP pixel-distortion displacement magnitude using unique degree-two-through-five coefficient terms and offsets from CRPIX. No WCS celestial projection, inverse fit or catalog registration. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sip-astrometric-pixel-distortion-record) · [Technical reference](https://fits.gsfc.nasa.gov/registry/sip/SIP_distortion_v1_0.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "xOffset": 2,
      "yOffset": 3,
      "aTerms": [
        {
          "i": 2,
          "j": 0,
          "coefficient": 0.1
        }
      ],
      "bTerms": [
        {
          "i": 0,
          "j": 2,
          "coefficient": 0.1
        }
      ],
      "observedValue": 0.9848857801796105,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.9848857801796105,
  "/records/0/observedValue": 0.9848857801796105,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Narrowband Broadband Continuum Line Record

Service ID: `narrowband-broadband-continuum-line-record`. USD 9.00 per job.

Separate line count rate from a flat-continuum narrow/broadband pair including declared line leakage into the broad band. No spectral calibration, continuum-slope fit or astrophysical line identification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Throughput ratio is an effective count-rate response for the supplied flat-continuum linear mixture. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=narrowband-broadband-continuum-line-record) · [Technical reference](https://irtfweb.ifa.hawaii.edu/~cushing/downloads/mcc_photometry.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "narrowCounts": 10,
      "broadCounts": 20,
      "narrowSeconds": 1,
      "broadSeconds": 1,
      "narrowWidth": 1,
      "broadWidth": 2,
      "throughputRatio": 1,
      "lineResponseRatio": 0,
      "observedValue": 0,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0,
  "/records/0/observedValue": 0,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Ccm89 Optical Extinction Band Record

Service ID: `ccm89-optical-extinction-band-record`. USD 9.00 per job.

Evaluate CCM89 optical extinction in magnitudes at a supplied inverse wavelength, Rv and colour excess. Only the optical polynomial interval is supported; no dust-map lookup or extinction measurement. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ccm89-optical-extinction-band-record) · [Technical reference](https://dust-extinction.readthedocs.io/en/stable/_modules/dust_extinction/parameter_averages.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inverseMicrons": 1.82,
      "rv": 3.1,
      "colourExcess": 1,
      "observedValue": 3.1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 3.1,
  "/records/0/observedValue": 3.1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Balmer Decrement Reddening Reconciliation Record

Service ID: `balmer-decrement-reddening-reconciliation-record`. USD 9.00 per job.

Reconcile a screen colour excess from an observed and supplied intrinsic H-alpha/H-beta line ratio and explicit extinction coefficients. Negative excess is preserved; no case-B parameter choice or plasma diagnosis. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=balmer-decrement-reddening-reconciliation-record) · [Technical reference](https://learn.astropy.org/tutorials/color-excess.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "observedHaHb": 6,
      "intrinsicHaHb": 3,
      "kHb": 2,
      "kHa": 1,
      "observedValue": 0.752574989159953,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.752574989159953,
  "/records/0/observedValue": 0.752574989159953,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Stellar Curve Of Growth Aperture Correction Record

Service ID: `stellar-curve-of-growth-aperture-correction-record`. USD 9.00 per job.

Reconcile the magnitude aperture correction from measured concentric annular background-subtracted fluxes to a larger finite reference aperture. No infinite-aperture/PSF extrapolation or photometric standard claim. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=stellar-curve-of-growth-aperture-correction-record) · [Technical reference](https://photutils.readthedocs.io/en/stable/user_guide/aperture.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "annulusFluxes": [
        3,
        1
      ],
      "scienceAnnulusCount": 1,
      "observedValue": -0.3123468415207498,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": -0.3123468415207498,
  "/records/0/observedValue": -0.3123468415207498,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Lightcurve Intrinsic Fractional Rms Record

Service ID: `lightcurve-intrinsic-fractional-rms-record`. USD 9.00 per job.

Reconcile intrinsic fractional RMS from sample light-curve variance minus mean squared measurement error. Negative excess variance rejects rather than manufacturing variability; no significance or source classification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lightcurve-intrinsic-fractional-rms-record) · [Technical reference](https://heasarc.gsfc.nasa.gov/docs/software/lheasoft/help/powspec.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "fluxes": [
        1,
        3
      ],
      "errors": [
        0,
        0
      ],
      "observedValue": 0.7071067811865476,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.7071067811865476,
  "/records/0/observedValue": 0.7071067811865476,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Finite Exposure Trapezoid Transit Average Record

Service ID: `finite-exposure-trapezoid-transit-average-record`. USD 9.00 per job.

Integrate a symmetric trapezoid transit template over one finite exposure, including ingress/egress clipping. Parameters are supplied in common time units; no orbit fit, timing standard conversion or planet detection. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-exposure-trapezoid-transit-average-record) · [Technical reference](https://arxiv.org/html/1001.2010)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "depth": 0.2,
      "flatHalfDuration": 1,
      "ingressDuration": 1,
      "midtime": 0,
      "exposureStart": 1,
      "exposureEnd": 2,
      "observedValue": 0.9,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.9,
  "/records/0/observedValue": 0.9,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Transit Ephemeris Cycle Oc Record

Service ID: `transit-ephemeris-cycle-oc-record`. USD 9.00 per job.

Reconcile the mean observed-minus-calculated transit timing residual at explicitly supplied integer cycles. Times must already share one scale and barycentric convention; no cycle selection, ephemeris fit or timing-discovery claim. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=transit-ephemeris-cycle-oc-record) · [Technical reference](https://arxiv.org/html/1001.2010)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "epoch": 10,
      "period": 2,
      "observedMidtimes": [
        10.1,
        14.3
      ],
      "cycles": [
        0,
        2
      ],
      "observedValue": 0.2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.2,
  "/records/0/observedValue": 0.2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Asteroid Hg Absolute Magnitude Record

Service ID: `asteroid-hg-absolute-magnitude-record`. USD 9.00 per job.

Reconcile asteroid absolute magnitude using the full Bowell1989 A4 H,G short-angle rational and long-angle exponential blend over supplied phase angles from 0 to 150 degrees. Distances are in au; supplied G is not estimated. Phase correction is retained separately with stable log algebra. No HG12/HG1G2 substitution, physical diameter or actual asteroid calibration. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=asteroid-hg-absolute-magnitude-record) · [Technical reference](https://sbpy.readthedocs.io/en/latest/_modules/sbpy/photometry/iau.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "apparentMagnitude": 10,
      "heliocentricAu": 1,
      "observerAu": 1,
      "phaseDegrees": 0,
      "slopeG": 0.15,
      "observedValue": 10,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 10,
  "/records/0/observedValue": 10,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Comet Afrho Aperture Dust Proxy Record

Service ID: `comet-afrho-aperture-dust-proxy-record`. USD 9.00 per job.

Reconcile the comet Af-rho dust proxy in centimetres from a same-band solar-normalized aperture flux and declared projected aperture radius. No phase correction, gas contamination or dust production rate is inferred. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=comet-afrho-aperture-dust-proxy-record) · [Technical reference](https://sbpy.readthedocs.io/en/latest/api/sbpy.activity.dust.Afrho.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cometToSolarFlux": 0.25,
      "heliocentricAu": 1,
      "observerDistanceCm": 2,
      "apertureRadiusCm": 1,
      "observedValue": 4,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 4,
  "/records/0/observedValue": 4,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Lambert Reflected Planet Phase Flux Record

Service ID: `lambert-reflected-planet-phase-flux-record`. USD 9.00 per job.

Reconcile reflected planet-to-star flux under a Lambert-sphere phase function and explicit geometric albedo. Thermal light, eccentric separation variation and real planet characterization are excluded. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lambert-reflected-planet-phase-flux-record) · [Technical reference](https://arxiv.org/html/1001.2010)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "geometricAlbedo": 0.5,
      "radiusOverSeparation": 0.1,
      "phaseDegrees": 90,
      "observedValue": 0.0015915494309189536,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.0015915494309189536,
  "/records/0/observedValue": 0.0015915494309189536,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Small Starspot Projected Modulation Record

Service ID: `small-starspot-projected-modulation-record`. USD 9.00 per job.

Reconcile sampled peak-to-peak relative modulation of one infinitesimal dark starspot with linear limb darkening. Spot area is a fraction of full stellar surface; no finite-spot occultation or magnetic inference. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=small-starspot-projected-modulation-record) · [Technical reference](https://arxiv.org/html/1001.2010)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "spotAreaFraction": 0.01,
      "contrast": 0,
      "spotLatitudeDegrees": 0,
      "viewInclinationDegrees": 90,
      "limbCoefficient": 0,
      "rotationPhasesDegrees": [
        0,
        90,
        180
      ],
      "observedValue": 0.04,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.04,
  "/records/0/observedValue": 0.04,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Double Lined Binary Dynamical Mass Record

Service ID: `double-lined-binary-dynamical-mass-record`. USD 9.00 per job.

Reconcile total dynamical mass of a double-lined Keplerian binary from period, velocity semiamplitudes, eccentricity and explicit inclination. Units must match G; no inclination fit or object classification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=double-lined-binary-dynamical-mass-record) · [Technical reference](https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_%28Tatum%29/18%3A_Spectroscopic_Binary_Stars/18.04%3A_Masses)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "period": 6.283185307179586,
      "semiAmplitudeA": 1,
      "semiAmplitudeB": 1,
      "eccentricity": 0,
      "inclinationDegrees": 90,
      "gravityConstant": 1,
      "observedValue": 8,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 8,
  "/records/0/observedValue": 8,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Thin Accretion Disk Radial Temperature Record

Service ID: `thin-accretion-disk-radial-temperature-record`. USD 9.00 per job.

Reconcile effective temperature of a steady optically thick thin accretion disk with zero inner-edge torque. Newtonian nonrelativistic model only; no mass-accretion inference or spectral fit. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=thin-accretion-disk-radial-temperature-record) · [Technical reference](https://astro.cas.cz/bursa/presentations/2107-xdas-workshop-opava/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gravityConstant": 1,
      "centralMass": 1,
      "accretionRate": 8.377580409572781,
      "innerRadius": 1,
      "radius": 4,
      "stefanBoltzmann": 1,
      "observedValue": 0.29730177875068026,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.29730177875068026,
  "/records/0/observedValue": 0.29730177875068026,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Projected Virial Cluster Mass Record

Service ID: `projected-virial-cluster-mass-record`. USD 9.00 per job.

Reconcile a projected virial mass estimator from supplied member velocities and pairwise projected separations. Assumes equilibrium, membership and isotropic sampling; no measured cluster mass or bound-system certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=projected-virial-cluster-mass-record) · [Technical reference](https://articles.adsabs.harvard.edu/pdf/1985ApJ...298....8H)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lineVelocities": [
        -1,
        0,
        1
      ],
      "projectedPositions": [
        [
          0,
          0
        ],
        [
          1,
          0
        ],
        [
          0,
          1
        ]
      ],
      "gravityConstant": 1,
      "observedValue": 10.444484155115322,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 10.444484155115322,
  "/records/0/observedValue": 10.444484155115322,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Sersic Galaxy Aperture Flux Record

Service ID: `sersic-galaxy-aperture-flux-record`. USD 9.00 per job.

Reconcile elliptical-aperture flux by radial quadrature of a supplied Sersic-form profile with an explicit bn and reference radius, which is not necessarily a half-light radius. No automatic half-light coefficient, PSF convolution, background fit or galaxy classification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sersic-galaxy-aperture-flux-record) · [Technical reference](https://docs.astropy.org/en/stable/api/astropy.modeling.functional_models.Sersic1D.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "referenceRadius": 1,
      "referenceIntensity": 1,
      "index": 1,
      "bn": 1,
      "apertureRadius": 1,
      "axisRatio": 1,
      "observedValue": 4.51309783098796,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 4.51309783098796,
  "/records/0/observedValue": 4.51309783098796,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Doppler Absorption Curve Of Growth Record

Service ID: `doppler-absorption-curve-of-growth-record`. USD 9.00 per job.

Reconcile equivalent width of a purely Doppler-broadened absorption line under a uniform screen by bounded profile integration. No damping wings, oscillator strength conversion or column-density fit. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=doppler-absorption-curve-of-growth-record) · [Technical reference](https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Stellar_Atmospheres_(Tatum)/11:_Curve_of_Growth/11.04:_Curve_of_Growth_for_Gaussian_Profiles)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "centralOpticalDepth": 0,
      "dopplerWidth": 1,
      "integrationHalfWidths": 6,
      "observedValue": 0,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0,
  "/records/0/observedValue": 0,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Pulsar Dispersion Delay Epoch Record

Service ID: `pulsar-dispersion-delay-epoch-record`. USD 9.00 per job.

Fit a common pulse epoch plus cold-plasma inverse-frequency-squared delay and reconcile arrival at a declared reference frequency. Frequency and dispersion units must match; no raw radio processing, timing-clock or pulsar identity validation. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pulsar-dispersion-delay-epoch-record) · [Technical reference](https://www.jb.man.ac.uk/research/pulsar/Education/Tutorial/tut/node14.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "observations": [
        {
          "frequency": 1,
          "arrivalTime": 5
        },
        {
          "frequency": 2,
          "arrivalTime": 2
        },
        {
          "frequency": 4,
          "arrivalTime": 1.25
        }
      ],
      "referenceFrequency": 2,
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Aspirated Psychrometer Vapour Pressure Record

Service ID: `aspirated-psychrometer-vapour-pressure-record`. USD 9.00 per job.

Reduce an aspirated liquid-water psychrometer observation to vapour pressure in kPa with a supplied psychrometer coefficient. Not the constant-enthalpy wet-bulb model; no instrument calibration or heat-stress advice. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=aspirated-psychrometer-vapour-pressure-record) · [Technical reference](https://www.fao.org/4/x0490e/x0490e06.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "dryBulbC": 20,
      "wetBulbC": 20,
      "pressureKpa": 100,
      "psychrometerCoefficient": 0.00066,
      "observedValue": 2.338281270927446,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2.338281270927446,
  "/records/0/observedValue": 2.338281270927446,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Sonic Temperature Humidity Correction Record

Service ID: `sonic-temperature-humidity-correction-record`. USD 9.00 per job.

Reconcile actual air temperature in K from supplied sonic temperature under the stated first-order specific-humidity correction. No crosswind or acoustic-path correction is inferred. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sonic-temperature-humidity-correction-record) · [Technical reference](https://amt.copernicus.org/articles/18/5527/2025/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sonicTemperatureK": 301.53,
      "specificHumidity": 0.01,
      "observedValue": 300,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 300,
  "/records/0/observedValue": 300,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Pressure Layer Precipitable Water Record

Service ID: `pressure-layer-precipitable-water-record`. USD 9.00 per job.

Integrate specific humidity over a supplied decreasing-pressure column into precipitable water in kg/m2, numerically equal to mm. No extrapolation outside the sounding or precipitation forecast. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pressure-layer-precipitable-water-record) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.precipitable_water.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pressurePa": [
        100000,
        90000
      ],
      "specificHumidity": [
        0.01,
        0.01
      ],
      "gravity": 10,
      "observedValue": 10,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 10,
  "/records/0/observedValue": 10,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Sunphotometer Langley Aerosol Depth Record

Service ID: `sunphotometer-langley-aerosol-depth-record`. USD 9.00 per job.

Fit a Langley log-irradiance slope and subtract explicit Rayleigh and gas optical depths to reconcile aerosol optical depth. Stable atmosphere and cloud-free input are assumptions; no actual atmospheric clearance. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sunphotometer-langley-aerosol-depth-record) · [Technical reference](https://repository.library.noaa.gov/view/noaa/18346)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "observations": [
        {
          "airmass": 1,
          "irradiance": 0.36787944117144233
        },
        {
          "airmass": 2,
          "irradiance": 0.1353352832366127
        },
        {
          "airmass": 3,
          "irradiance": 0.049787068367863944
        }
      ],
      "rayleighDepth": 0.2,
      "gasDepth": 0.1,
      "observedValue": 0.7,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.7,
  "/records/0/observedValue": 0.7,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Wmo First Tropopause Supplied Profile Record

Service ID: `wmo-first-tropopause-supplied-profile-record`. USD 9.00 per job.

Reconcile the first sampled level satisfying the WMO thermal tropopause lapse criterion, including the full next 2 km with linear interpolation. Resolves supplied levels only; no second tropopause or radiosonde quality certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=wmo-first-tropopause-supplied-profile-record) · [Technical reference](https://amt.copernicus.org/articles/12/4113/2019/amt-12-4113-2019.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "heightsMetres": [
        0,
        1000,
        3000,
        5000
      ],
      "temperaturesKelvin": [
        290,
        280,
        278,
        276
      ],
      "observedValue": 1000,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1000,
  "/records/0/observedValue": 1000,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Scorer Parameter Three Level Record

Service ID: `scorer-parameter-three-level-record`. USD 9.00 per job.

Reduce the nonrotating two-dimensional Scorer parameter at a middle level using nonuniform-grid wind curvature and supplied buoyancy frequency squared. No mountain-wave amplitude, turbulence or aviation guidance. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=scorer-parameter-three-level-record) · [Technical reference](https://gibbs.science/teaching/mesoscale/handouts/lecture_notes_03.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "heights": [
        0,
        1,
        2
      ],
      "wind": [
        2,
        2,
        2
      ],
      "buoyancyFrequencySquared": 4,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Bowen Ratio Surface Energy Partition Record

Service ID: `bowen-ratio-surface-energy-partition-record`. USD 9.00 per job.

Reconcile latent heat flux using the Bowen-ratio energy-balance method with equal turbulent transfer coefficients. Available energy already excludes storage; no eddy-covariance validation or evapotranspiration advice. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bowen-ratio-surface-energy-partition-record) · [Technical reference](https://www.fao.org/4/x0490e/x0490e06.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "availableEnergy": 100,
      "temperatureDifference": 1,
      "vapourPressureDifference": 0.2,
      "psychrometricKpaC": 0.1,
      "observedValue": 66.66666666666667,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 66.66666666666667,
  "/records/0/observedValue": 66.66666666666667,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Disdrometer Bin Rainfall Rate Record

Service ID: `disdrometer-bin-rainfall-rate-record`. USD 9.00 per job.

Reconcile rain rate in mm/h from bin-integrated drop number concentrations, measured terminal speeds and spherical drop volumes. Concentrations are per bin rather than per diameter width; no drop classification or radar retrieval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=disdrometer-bin-rainfall-rate-record) · [Technical reference](https://www.eoas.ubc.ca/books/Practical_Meteorology/prmet102/Ch07-precipitation-v102b.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "bins": [
        {
          "diameterMm": 1,
          "numberPerM3": 1,
          "fallSpeedMSecond": 1
        }
      ],
      "observedValue": 0.0018849555921538756,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.0018849555921538756,
  "/records/0/observedValue": 0.0018849555921538756,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Canopy Interception Explicit Drainage Record

Service ID: `canopy-interception-explicit-drainage-record`. USD 9.00 per job.

Reconcile throughfall plus drainage for an explicitly declared one-step canopy bucket with exponential drainage at or above canopy capacity and bounded evaporation. This is the stated supplied scenario model, not a calibrated Rutter parameterization or forest water forecast. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=canopy-interception-explicit-drainage-record) · [Technical reference](https://web.mit.edu/people/eltahir/www/a_jcli93a_files/1993%20Eltahir%20Bras%20rainfall%20intercept%20JClimate.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "initialStorage": 1,
      "rainfall": 2,
      "freeThroughfallFraction": 0.5,
      "capacity": 2,
      "evaporationPotential": 0,
      "drainageCoefficient": 1,
      "drainageExponent": 1,
      "stepTime": 1,
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Isotropic Sky Tilted Pyranometer Record

Service ID: `isotropic-sky-tilted-pyranometer-record`. USD 9.00 per job.

Reconcile ideal plane-of-array irradiance with an isotropic diffuse sky and Lambertian ground reflection. Incidence is supplied, not derived from an ephemeris; no PV electrical yield or irradiance measurement certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=isotropic-sky-tilted-pyranometer-record) · [Technical reference](https://pvlib-python.readthedocs.io/en/stable/reference/generated/pvlib.irradiance.isotropic.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "directNormal": 100,
      "diffuseHorizontal": 20,
      "globalHorizontal": 100,
      "incidenceDegrees": 0,
      "tiltDegrees": 0,
      "groundAlbedo": 0.2,
      "observedValue": 120,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 120,
  "/records/0/observedValue": 120,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Rock Core Rqd Run Reconciliation Record

Service ID: `rock-core-rqd-run-reconciliation-record`. USD 9.00 per job.

Reconcile standard RQD percentage using sound natural-break core pieces at least 100 mm long against the drilled run. Soundness and break classification are supplied; no rock-mass rating or engineering approval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rock-core-rqd-run-reconciliation-record) · [Technical reference](https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA207597.xhtml)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "runLengthMetres": 1,
      "soundPieceLengthsMetres": [
        0.4,
        0.3,
        0.05,
        0.05
      ],
      "observedValue": 70,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 70,
  "/records/0/observedValue": 70,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Terzaghi Joint Scanline Orientation Record

Service ID: `terzaghi-joint-scanline-orientation-record`. USD 9.00 per job.

Reconcile a Terzaghi orientation-weighted joint count from unit plane normals and a unit scanline. A declared minimum intersection cosine rejects near-blind joints rather than silently capping weights; no inferred unseen fracture set. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=terzaghi-joint-scanline-orientation-record) · [Technical reference](https://www.rocscience.com/help/dips/v9/documentation/analysis/weighting/terzaghi-weighting)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "scanlineDirection": [
        1,
        0,
        0
      ],
      "jointNormals": [
        [
          1,
          0,
          0
        ],
        [
          0.5,
          0.8660254037844386,
          0
        ]
      ],
      "minimumCosine": 0.1,
      "observedValue": 3,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 3,
  "/records/0/observedValue": 3,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Relative Gravimeter Base Loop Drift Record

Service ID: `relative-gravimeter-base-loop-drift-record`. USD 9.00 per job.

Reconcile a relative gravity reading to the loop-start instrumental baseline using linear base-station drift and an explicitly additive supplied tide correction. No absolute gravity, drift extrapolation or tide model retrieval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=relative-gravimeter-base-loop-drift-record) · [Technical reference](https://geoscienceaustralia.github.io/galileoQC/tutorials/Gravimeter_Corrections.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "baseStartTime": 0,
      "baseEndTime": 10,
      "baseStartReading": 1,
      "baseEndReading": 3,
      "fieldTime": 5,
      "fieldReading": 10,
      "tideCorrection": 0.5,
      "observedValue": 9.5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 9.5,
  "/records/0/observedValue": 9.5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Marine Gravity Eotvos Motion Record

Service ID: `marine-gravity-eotvos-motion-record`. USD 9.00 per job.

Reconcile the spherical Eotvos correction to apparent gravity from east/north ground velocity in a rotating frame. Positive east convention and common SI units; no navigation/latitude or gravimeter validation. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=marine-gravity-eotvos-motion-record) · [Technical reference](https://geoscienceaustralia.github.io/galileoQC/tutorials/Gravimeter_Corrections.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "eastSpeed": 1,
      "northSpeed": 2,
      "latitudeDegrees": 0,
      "rotationRate": 1,
      "earthRadius": 10,
      "observedValue": 2.5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2.5,
  "/records/0/observedValue": 2.5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Larionov Young Rock Gamma Shale Record

Service ID: `larionov-young-rock-gamma-shale-record`. USD 9.00 per job.

Reconcile the Larionov young-rock empirical shale-volume estimate from a normalized gamma-ray index. Endpoint lithologies and formula choice are supplied; no mineral identification or reservoir certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=larionov-young-rock-gamma-shale-record) · [Technical reference](https://petroleumoffice.com/lambda/po.lm.pp.vsh.larionov.tertiary)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gamma": 1,
      "cleanGamma": 0,
      "shaleGamma": 2,
      "observedValue": 0.21621515358679566,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.21621515358679566,
  "/records/0/observedValue": 0.21621515358679566,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Coupled Sonic Density Three Phase Depth Profile Report

Service ID: `coupled-sonic-density-three-phase-depth-profile-report`. USD 9.00 per job.

Reconcile a depth-indexed sonic and bulk-density profile under a declared three-volume mixture of two supplied matrix minerals and pore fluid. Solve volume closure plus linear transit-time and density balances at every depth, reject unresolved endmembers or infeasible fractions, retain reconstructed logs/residuals, and integrate phase columns and phase transit contributions. Transit time uses the explicitly extended Wyllie time-average assumption; density follows volume/mass conservation. Between depths, fractions/logs use the declared piecewise-linear average-end integration. Coherent depth/transit/density units; no gas, shale, compaction, mineral identification, physical porosity validation or reservoir classification. Observed value is integrated pore column. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=coupled-sonic-density-three-phase-depth-profile-report) · [Technical reference](https://sep.stanford.edu/oldsep/matt/sdi/fd/Fig/paper_html/node11.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "matrix1Transit": 1,
      "matrix2Transit": 2,
      "fluidTransit": 4,
      "matrix1Density": 3,
      "matrix2Density": 4,
      "fluidDensity": 1,
      "depths": [
        0,
        4
      ],
      "bulkTransitTimes": [
        2,
        2.75
      ],
      "bulkDensities": [
        2.75,
        2.25
      ],
      "observedValue": 1.5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1.5,
  "/records/0/matrix1Fractions": [
    0.5,
    0.25
  ],
  "/records/0/matrix2Fractions": [
    0.25,
    0.25
  ],
  "/records/0/poreFractions": [
    0.25,
    0.5
  ],
  "/records/0/reconstructedTransitTimes": [
    2,
    2.75
  ],
  "/records/0/reconstructedDensities": [
    2.75,
    2.25
  ],
  "/records/0/transitResiduals": [
    0,
    0
  ],
  "/records/0/densityResiduals": [
    0,
    0
  ],
  "/records/0/closureResiduals": [
    0,
    0
  ],
  "/records/0/matrix1Column": 1.5,
  "/records/0/matrix2Column": 1,
  "/records/0/poreColumn": 1.5,
  "/records/0/phaseTransitContributions": [
    1.5,
    2,
    6
  ],
  "/records/0/integratedTransitTime": 9.5,
  "/records/0/integratedDensity": 10,
  "/records/0/columnClosureResidual": 0,
  "/records/0/transitBalanceResidual": 0,
  "/records/0/densityBalanceResidual": 0,
  "/records/0/observedValue": 1.5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Liquid Pycnometer Rock Grain Density Record

Service ID: `liquid-pycnometer-rock-grain-density-record`. USD 9.00 per job.

Reconcile rock grain density by liquid pycnometer displaced mass using a matched-temperature liquid density. No trapped-air, dissolution or balance buoyancy correction is inferred. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=liquid-pycnometer-rock-grain-density-record) · [Technical reference](https://rosap.ntl.bts.gov/view/dot/26937/dot_26937_DS1.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "drySolidMass": 2,
      "bottleLiquidMass": 10,
      "bottleSolidLiquidMass": 11,
      "liquidDensity": 1,
      "observedValue": 2,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2,
  "/records/0/observedValue": 2,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Brazilian Rock Disc Tensile Strength Record

Service ID: `brazilian-rock-disc-tensile-strength-record`. USD 9.00 per job.

Reconcile nominal Brazilian splitting tensile strength of a diametrically loaded rock disc. Units follow load/length squared; valid failure mode and specimen preparation are supplied, not certified. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=brazilian-rock-disc-tensile-strength-record) · [Technical reference](https://static.rocscience.cloud/assets/resources/learning/hoek/3.-Intact-rock-strength_2023-06-30-120556_xiuv.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "failureLoad": 3.141592653589793,
      "diameter": 2,
      "thickness": 1,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Rock Point Load Size Corrected Index Record

Service ID: `rock-point-load-size-corrected-index-record`. USD 9.00 per job.

Reconcile the standard size-corrected Is(50) point-load index from failure load in N and equivalent diameter in mm, yielding MPa. No UCS conversion or rock-strength certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rock-point-load-size-corrected-index-record) · [Technical reference](https://gaeatech.com/public/Manuals/GaeaSynergy/gdms_point_load_calculations.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "failureLoad": 2500,
      "equivalentDiameterMm": 50,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Klinkenberg Gas Permeability Extrapolation Record

Service ID: `klinkenberg-gas-permeability-extrapolation-record`. USD 9.00 per job.

Fit the Klinkenberg apparent-permeability versus inverse-absolute-pressure relation and reconcile its infinite-pressure intercept. No pore-network, nonlinear slip or intrinsic liquid-permeability validation. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=klinkenberg-gas-permeability-extrapolation-record) · [Technical reference](https://wipp.energy.gov/information_repository/cra/2009_cra/references/Others/Klinkenberg_1941_The_Permeability_of_Porous_Media_ERMS208556.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "measurements": [
        {
          "meanAbsolutePressure": 1,
          "apparentPermeability": 3
        },
        {
          "meanAbsolutePressure": 2,
          "apparentPermeability": 2
        },
        {
          "meanAbsolutePressure": 4,
          "apparentPermeability": 1.5
        }
      ],
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Corrected Mercury Intrusion Pore Volume Curve Report

Service ID: `corrected-mercury-intrusion-pore-volume-curve-report`. USD 9.00 per job.

Reconcile a complete strictly increasing pressure/intrusion curve using supplied blank volumes and a separately supplied linear apparent-compression volume correction Vbulk*k*(P-Pfirst). Require a zero corrected baseline and nondecreasing corrected pore volume within supplied bulk volume. Convert Washburn entry radii, retain interval pore volumes and positive bin densities DeltaV/abs(DeltaLog10(radius)), and calculate volume quantiles under an explicitly uniform-log-radius distribution within each measured pressure bin. Surface tension in N/m and pressure in Pa give radius metres; all volumes share one unit. No complete manufacturer compression algorithm, ink-bottle correction, pore topology or true-size certification. Observed value is total corrected intrusion volume. The supplied additional compression term must not duplicate a contribution already included in the supplied blank. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=corrected-mercury-intrusion-pore-volume-curve-report) · [Technical reference](https://downloads.micromeritics.com/Guides/AutoPore-IV-9500-Operator-Manual-Rev-A-Nov-2018.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "surfaceTension": 1,
      "contactAngleDegrees": 120,
      "pressures": [
        1,
        2,
        4
      ],
      "measuredCumulativeVolumes": [
        0,
        2.6,
        5.3
      ],
      "blankCumulativeVolumes": [
        0,
        0.5,
        1
      ],
      "bulkVolume": 10,
      "additionalApparentCompressibility": 0.01,
      "volumeQuantiles": [
        0.25,
        0.5,
        0.75
      ],
      "observedValue": 4,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 4,
  "/records/0/entryRadii": [
    1,
    0.5,
    0.25
  ],
  "/records/0/corrections": [
    0,
    0.6,
    1.3
  ],
  "/records/0/correctedCumulativeVolumes": [
    0,
    2,
    4
  ],
  "/records/0/incrementalVolumes": [
    2,
    2
  ],
  "/records/0/log10VolumeDensities": [
    6.643856189774724,
    6.643856189774724
  ],
  "/records/0/quantileEntryRadii": [
    0.7071067811865476,
    0.5,
    0.3535533905932738
  ],
  "/records/0/totalIntrudedVolume": 4,
  "/records/0/intrudedPorosity": 0.4,
  "/records/0/volumeBalanceResidual": 0,
  "/records/0/observedValue": 4,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Leverett J Capillary Pressure Reconciliation Record

Service ID: `leverett-j-capillary-pressure-reconciliation-record`. USD 9.00 per job.

Reconcile a Leverett J capillary pressure using supplied porosity, permeability and wetting-fluid properties. No universal J curve selection, saturation matching or reservoir forecast. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=leverett-j-capillary-pressure-reconciliation-record) · [Technical reference](https://opm.github.io/opm-flow-editor-support/keywords/JFUNC.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "jValue": 2,
      "porosity": 0.25,
      "permeability": 1,
      "surfaceTension": 1,
      "contactAngleDegrees": 0,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Atterberg Cup Flow Curve Liquid Limit Record

Service ID: `atterberg-cup-flow-curve-liquid-limit-record`. USD 9.00 per job.

Reduce cup-method moisture trials to a log-blow flow curve and reconcile the 25-blow liquid limit in percent. No plastic limit, soil classification or compliance certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=atterberg-cup-flow-curve-liquid-limit-record) · [Technical reference](https://rosap.ntl.bts.gov/view/dot/26937/dot_26937_DS1.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "trials": [
        {
          "blows": 10,
          "wetMass": 1.4,
          "dryMass": 1,
          "tareMass": 0
        },
        {
          "blows": 25,
          "wetMass": 1.3,
          "dryMass": 1,
          "tareMass": 0
        },
        {
          "blows": 50,
          "wetMass": 1.224352920263397,
          "dryMass": 1,
          "tareMass": 0
        }
      ],
      "observedValue": 30,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 30,
  "/records/0/observedValue": 30,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Direct Shear Area Corrected Failure Envelope Record

Service ID: `direct-shear-area-corrected-failure-envelope-record`. USD 9.00 per job.

Fit a linear Mohr-Coulomb direct-shear envelope after overlap-area correction and reconcile shear strength at supplied normal stress. No pore-pressure correction, failure criterion selection or geotechnical approval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Retain specimen overlap areas, normal/shear stresses, fitted cohesion/friction angle and each fitted stress/residual plus RMS. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=direct-shear-area-corrected-failure-envelope-record) · [Technical reference](https://archive.nptel.ac.in/content/storage2/courses/105106055/Mod2/Lecture5.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "specimens": [
        {
          "initialLength": 2,
          "width": 1,
          "horizontalDisplacement": 1,
          "normalLoad": 1,
          "shearLoad": 2
        },
        {
          "initialLength": 2,
          "width": 1,
          "horizontalDisplacement": 1,
          "normalLoad": 2,
          "shearLoad": 3
        },
        {
          "initialLength": 2,
          "width": 1,
          "horizontalDisplacement": 1,
          "normalLoad": 3,
          "shearLoad": 4
        }
      ],
      "targetNormalStress": 4,
      "observedValue": 5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 5,
  "/records/0/observedValue": 5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false,
  "/records/0/overlapAreas": [
    1,
    1,
    1
  ],
  "/records/0/normalStresses": [
    1,
    2,
    3
  ],
  "/records/0/shearStresses": [
    2,
    3,
    4
  ],
  "/records/0/cohesionIntercept": 1,
  "/records/0/frictionAngleDegrees": 45,
  "/records/0/predictedShearStresses": [
    2,
    3,
    4
  ],
  "/records/0/shearResiduals": [
    0,
    0,
    0
  ],
  "/records/0/shearRootMeanSquareResidual": 0
}
```

## Sea Ice Brine Volume Fraction Record

Service ID: `sea-ice-brine-volume-fraction-record`. USD 9.00 per job.

Reconcile the Frankenstein-Garner empirical sea-ice brine volume fraction over its declared temperature profile. No connected brine, ice strength, permeability or travel-safety claim. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sea-ice-brine-volume-fraction-record) · [Technical reference](https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000020244)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "temperatureC": -5,
      "salinityPerMille": 5,
      "observedValue": 0.051845,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.051845,
  "/records/0/observedValue": 0.051845,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Terzaghi Staged Load Consolidation History Record

Service ID: `terzaghi-staged-load-consolidation-history-record`. USD 9.00 per job.

Reconcile a full staged-load settlement history by superposition of Terzaghi one-dimensional consolidation degrees for a homogeneous constant-coefficient layer. Drainage length fixes single/double drainage; ultimate settlement increments may include unloading. No stress-dependent coefficient, secondary creep, parameter fit or foundation approval. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=terzaghi-staged-load-consolidation-history-record) · [Technical reference](https://static.rocscience.cloud/assets/verification-and-theory/RS2/RS2-Consolidation-Verification.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "drainageLength": 1,
      "consolidationCoefficient": 1,
      "loads": [
        {
          "time": 0,
          "ultimateSettlement": 1
        }
      ],
      "observationTimes": [
        0,
        100
      ],
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/settlements": [
    0,
    1
  ],
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Cpt Coupled Stress Normalization Profile Record

Service ID: `cpt-coupled-stress-normalization-profile-record`. USD 9.00 per job.

Reconcile the final supplied-depth CPT behavior index while retaining the complete profile of coupled normalized tip resistance, friction ratio and stress exponent. Robertson stress exponent and behavior index are solved together. Pressures share units; no categorical soil identification, liquefaction resistance or ground suitability claim. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cpt-coupled-stress-normalization-profile-record) · [Technical reference](https://www.cpt-robertson.com/PublicationsPDF/Robertson%202010%20Insitu%20State%20CPT10%20cor.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "atmosphericPressure": 1,
      "profile": [
        {
          "correctedTip": 101,
          "sleeveFriction": 1,
          "totalVertical": 1,
          "effectiveVertical": 1
        },
        {
          "correctedTip": 11,
          "sleeveFriction": 0.1,
          "totalVertical": 1,
          "effectiveVertical": 1
        }
      ],
      "observedValue": 2.754868417910373,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 2.754868417910373,
  "/records/0/indices": [
    1.9103141102970473,
    2.754868417910373
  ],
  "/records/0/normalizedTips": [
    100,
    10
  ],
  "/records/0/observedValue": 2.754868417910373,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Homogeneous Sp Pick Distance Record

Service ID: `homogeneous-sp-pick-distance-record`. USD 9.00 per job.

Reconcile hypocentral path distance from S-minus-P picks in an explicitly homogeneous common-ray medium. No origin location, layered travel-time table or earthquake detection claim. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=homogeneous-sp-pick-distance-record) · [Technical reference](https://gpg.geosci.xyz/content/seismic/traveltimes.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pArrival": 1,
      "sArrival": 2,
      "pSpeed": 6,
      "sSpeed": 3,
      "observedValue": 6,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 6,
  "/records/0/observedValue": 6,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Seismic Array Plane Wave Slowness Record

Service ID: `seismic-array-plane-wave-slowness-record`. USD 9.00 per job.

Fit a free epoch and east/north horizontal slowness to coherent supplied planar arrival picks. Retain fitted epoch/slownesses, each predicted arrival and signed residual, arrival RMS, and the apparent horizontal speed discrepancy. This is an authored ordinary least-squares plane-arrival reduction, not a beamforming or wave-association implementation. No source backtracking, phase association or physical material wave speed interpretation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=seismic-array-plane-wave-slowness-record) · [Technical reference](https://docs.obspy.org/_modules/obspy/signal/array_analysis.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "stations": [
        {
          "east": 0,
          "north": 0,
          "arrival": 1
        },
        {
          "east": 1,
          "north": 0,
          "arrival": 3
        },
        {
          "east": 0,
          "north": 1,
          "arrival": 1
        }
      ],
      "observedValue": 0.5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.5,
  "/records/0/observedValue": 0.5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false,
  "/records/0/fittedEpoch": 1,
  "/records/0/eastSlowness": 2,
  "/records/0/northSlowness": 0,
  "/records/0/predictedArrivals": [
    1,
    3,
    1
  ],
  "/records/0/arrivalResiduals": [
    0,
    0,
    0
  ],
  "/records/0/arrivalRootMeanSquareResidual": 0
}
```

## Newmark Unilateral Sliding Block History Record

Service ID: `newmark-unilateral-sliding-block-history-record`. USD 9.00 per job.

Reconcile one-way rigid Newmark-block displacement for a supplied piecewise-constant driving-acceleration history and constant yield acceleration. Exactly resolve rest, sliding and stops inside intervals; preserve displacement and velocity histories. No yield-acceleration estimation, bidirectional friction, slope failure classification or hazard prediction. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=newmark-unilateral-sliding-block-history-record) · [Technical reference](https://www.rocscience.com/help/slide2/tutorials/tutorials-overview/seismic-analysis-with-newmark-method)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "yieldAcceleration": 1,
      "intervals": [
        {
          "duration": 1,
          "drivingAcceleration": 3
        },
        {
          "duration": 2,
          "drivingAcceleration": 0
        }
      ],
      "observedValue": 3,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 3,
  "/records/0/displacements": [
    1,
    3
  ],
  "/records/0/velocities": [
    2,
    0
  ],
  "/records/0/stoppingEpisodes": 1,
  "/records/0/observedValue": 3,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Pss78 Reference Temperature Salinometer Record

Service ID: `pss78-reference-temperature-salinometer-record`. USD 9.00 per job.

Reconcile practical salinity from conductivity ratio measured at exactly 15 degrees C IPTS-68 and atmospheric pressure by the PSS-78 reference-temperature polynomial. No temperature/pressure correction or TEOS-10 absolute salinity. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pss78-reference-temperature-salinometer-record) · [Technical reference](https://pythonhosted.org/seawater/eos80.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "conductivityRatio": 1,
      "observedValue": 35,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 35,
  "/records/0/observedValue": 35,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Zero Upcrossing Significant Wave Height Record

Service ID: `zero-upcrossing-significant-wave-height-record`. USD 9.00 per job.

Reconcile time-domain H one-third from complete zero-upcrossing waves about a supplied zero mean level. The highest-third count rounds up; incomplete end waves are excluded. No spectral Hm0 equivalence or sea-state forecast. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=zero-upcrossing-significant-wave-height-record) · [Technical reference](https://iadclexicon.org/significant-wave-height/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "times": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12
      ],
      "elevations": [
        0,
        1,
        0,
        -1,
        0,
        2,
        0,
        -2,
        0,
        3,
        0,
        -3,
        0
      ],
      "observedValue": 4,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 4,
  "/records/0/observedValue": 4,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Janus Adcp Four Beam Horizontal Speed Record

Service ID: `janus-adcp-four-beam-horizontal-speed-record`. USD 9.00 per job.

Reconcile horizontal speed from a symmetric four-beam Janus ADCP in its aligned instrument frame. Beam ordering is plus/minus first horizontal axis then plus/minus second; no tilt, compass or acoustic quality correction. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=janus-adcp-four-beam-horizontal-speed-record) · [Technical reference](https://www.teledynemarine.com/en-us/support/SiteAssets/RDI/Manuals%20and%20Guides/General%20Interest/Coordinate_Transformation.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "beamVelocities": [
        1.5,
        -1.5,
        2,
        -2
      ],
      "beamAngleDegrees": 30,
      "observedValue": 5,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 5,
  "/records/0/observedValue": 5,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Winkler Oxygen Titration Volume Record

Service ID: `winkler-oxygen-titration-volume-record`. USD 9.00 per job.

Reconcile dissolved oxygen in mg/L from a full-bottle Winkler titration with blank, reagent displacement and explicitly supplied reagent oxygen correction. Titrant standardization and reaction completion are supplied assumptions; no water-quality or laboratory certification. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=winkler-oxygen-titration-volume-record) · [Technical reference](https://hahana.soest.hawaii.edu/hot/protocols/chap5.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "titreMl": 1,
      "blankMl": 0,
      "thiosulfateNormality": 0.01,
      "bottleMl": 100,
      "reagentDisplacementMl": 0,
      "reagentOxygenMgL": 0,
      "observedValue": 0.8,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.8,
  "/records/0/observedValue": 0.8,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Plankton Net Flowmeter Filtered Density Record

Service ID: `plankton-net-flowmeter-filtered-density-record`. USD 9.00 per job.

Reconcile organisms per cubic metre for a plankton-net sample using calibrated through-water flowmeter distance and declared subsampling/filtration fractions. No taxonomy, net avoidance or ecological condition inference. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=plankton-net-flowmeter-filtered-density-record) · [Technical reference](https://www.fisheries.noaa.gov/inport/item/36201)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "organisms": 10,
      "subsampleFraction": 0.5,
      "rotations": 10,
      "metresPerRotation": 2,
      "mouthAreaM2": 1,
      "filtrationEfficiency": 1,
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Osborn Turbulent Diffusivity Layer Record

Service ID: `osborn-turbulent-diffusivity-layer-record`. USD 9.00 per job.

Reconcile thickness-mean Osborn diapycnal diffusivity from supplied dissipation and positive stratification with an explicit flux coefficient. No universal mixing-efficiency assumption, overturn detection or ocean-mixing validation. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=osborn-turbulent-diffusivity-layer-record) · [Technical reference](https://os.copernicus.org/articles/19/77/2023/index.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "layers": [
        {
          "thickness": 1,
          "dissipation": 2,
          "buoyancyFrequencySquared": 4
        },
        {
          "thickness": 1,
          "dissipation": 4,
          "buoyancyFrequencySquared": 4
        }
      ],
      "fluxCoefficient": 0.2,
      "observedValue": 0.15,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 0.15,
  "/records/0/observedValue": 0.15,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Deep Water Wave Encounter Period Record

Service ID: `deep-water-wave-encounter-period-record`. USD 9.00 per job.

Reconcile intrinsic deep-water wave period from vessel encounter period on the lower-frequency positive branch. Heading zero follows wave propagation; no current correction, vessel safety or observed-sea prediction. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=deep-water-wave-encounter-period-record) · [Technical reference](https://www.fossen.biz/publications/2015%20Belleter%20et%20al%20OE.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "encounterPeriod": 6.283185307179586,
      "vesselSpeed": 0,
      "headingToWaveDegrees": 0,
      "gravity": 1,
      "observedValue": 6.283185307179586,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 6.283185307179586,
  "/records/0/observedValue": 6.283185307179586,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Stommel Two Box Overturning Root Record

Service ID: `stommel-two-box-overturning-root-record`. USD 9.00 per job.

Reconcile a nonnegative equilibrium of the dimensionless Stommel thermohaline two-box model in an explicit root bracket. Other branches and stability are not inferred; no overturning-collapse forecast. Compare observedValue to calculatedValue with the supplied absolute tolerance in the stated units; equality to tolerance passes. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=stommel-two-box-overturning-root-record) · [Technical reference](https://courses.seas.harvard.edu/climate/eli/Courses/EPS131/Sources/07-AMOC/Papers/Stommel-1961.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "thermalForcing": 4,
      "salinityForcing": 2,
      "salinityRelaxation": 1,
      "rootBracket": [
        0.5,
        2
      ],
      "observedValue": 1,
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/calculatedValue": 1,
  "/records/0/observedValue": 1,
  "/records/0/tolerance": 1e-8,
  "/records/0/absoluteDifference": 0,
  "/records/0/mismatch": false
}
```

## Bowditch Closed Traverse Adjustment

Service ID: `bowditch-closed-traverse-adjustment`. USD 1.00 per job.

Balance a closed plane traverse by length-proportional Bowditch corrections; supplied bearings are clockwise from north. Coordinates start at zero; no boundary establishment. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bowditch-closed-traverse-adjustment) · [Technical reference](https://resources.arcgis.com/en/help/main/10.1/01m7/01m70000003v000000.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "legs": [
        {
          "length": 1,
          "azimuthDegrees": 0
        },
        {
          "length": 1,
          "azimuthDegrees": 90
        },
        {
          "length": 1,
          "azimuthDegrees": 180
        },
        {
          "length": 1,
          "azimuthDegrees": -90
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/perimeter": 4,
  "/records/0/closure": 0,
  "/records/0/finalEast": 0,
  "/records/0/finalNorth": 0
}
```

## Weighted Level Loop Closure Adjustment

Service ID: `weighted-level-loop-closure-adjustment`. USD 1.00 per job.

Adjust one independently observed level loop with supplied independent variances and fixed endpoint height difference. No network datum or instrument certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=weighted-level-loop-closure-adjustment) · [Technical reference](https://www.itl.nist.gov/div898/handbook/pmd/section4/pmd432.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "differences": [
        1,
        2
      ],
      "variances": [
        1,
        3
      ],
      "targetDifference": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/misclosure": 1,
  "/records/0/adjustedDifferences": [
    0.75,
    1.25
  ],
  "/records/0/adjustedTotal": 2
}
```

## Geopotential Layer Height Integration

Service ID: `geopotential-layer-height-integration`. USD 1.00 per job.

Integrate supplied leveled height increments times layer mean gravity into geopotential difference and dynamic height. No geoid interpolation, orthometric correction or datum certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=geopotential-layer-height-integration) · [Technical reference](https://www.ngs.noaa.gov/PUBS_LIB/TMNOSNGS34.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "heightSteps": [
        1,
        2
      ],
      "gravity": [
        9,
        10
      ],
      "referenceGravity": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/geopotentialDifference": 29,
  "/records/0/dynamicHeightDifference": 2.9
}
```

## Planar Unoriented Bearing-Line Fit

Service ID: `horizontal-resection-three-bearing-point`. USD 1.00 per job.

Fit a planar point from three unoriented absolute bearing lines by perpendicular-distance least squares. Bearings share one north reference and are equivalent under180-degree reversal. Forward-ray consistency, unknown instrument orientation, angular maximum likelihood and uncertainty estimation are excluded. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=horizontal-resection-three-bearing-point) · [Technical reference](https://ietresearch.onlinelibrary.wiley.com/doi/full/10.1049/rsn2.12520)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "stations": [
        {
          "east": 0,
          "north": 1,
          "bearingDegrees": 0
        },
        {
          "east": 1,
          "north": 0,
          "bearingDegrees": 90
        },
        {
          "east": -1,
          "north": 0,
          "bearingDegrees": -90
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/east": 0,
  "/records/0/north": 0,
  "/records/0/rmsPerpendicular": 0
}
```

## Utm Zone And Hemisphere Classification

Service ID: `utm-zone-and-hemisphere-classification`. USD 1.00 per job.

Classify geographic positions into standard UTM zones including Norway and Svalbard exceptions. No projected coordinates, datum lookup or EPSG code assertion. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=utm-zone-and-hemisphere-classification) · [Technical reference](https://raw.githubusercontent.com/geographiclib/geographiclib/main/src/UTMUPS.cpp)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "latitudeDegrees": 60,
      "longitudeDegrees": 6
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/zone": 32,
  "/records/0/hemisphere": "north",
  "/records/0/centralMeridianDegrees": 9
}
```

## Spherical Route Cross Track Station

Service ID: `spherical-route-cross-track-station`. USD 1.00 per job.

Resolve a point into signed cross-track distance and along-track station on a directed spherical great circle. Right of route is positive; excludes operational navigation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=spherical-route-cross-track-station) · [Technical reference](https://edwilliams.org/avform.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "radius": 1,
      "startLatitudeDegrees": 0,
      "startLongitudeDegrees": 0,
      "endLatitudeDegrees": 0,
      "endLongitudeDegrees": 90,
      "pointLatitudeDegrees": 30,
      "pointLongitudeDegrees": 45
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/crossTrack": -0.5235987755982988,
  "/records/0/alongTrack": 0.7853981633974483
}
```

## Geographic Antimeridian Polyline Split

Service ID: `geographic-antimeridian-polyline-split`. USD 1.00 per job.

Split a geographic polyline at the antimeridian using declared straight longitude/latitude segments and shortest longitude wrapping. This is not a geodesic interpolation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=geographic-antimeridian-polyline-split) · [Technical reference](https://www.rfc-editor.org/rfc/rfc7946#section-3.1.9)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "points": [
        {
          "longitude": 170,
          "latitude": 0
        },
        {
          "longitude": -170,
          "latitude": 20
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/segments": [
    [
      [
        170,
        0
      ],
      [
        180,
        10
      ]
    ],
    [
      [
        -180,
        10
      ],
      [
        -170,
        20
      ]
    ]
  ],
  "/records/0/crossings": 1
}
```

## Somigliana Normal Gravity Reference

Service ID: `somigliana-normal-gravity-reference`. USD 1.00 per job.

Evaluate the Somigliana reference-ellipsoid surface gravity formula from explicit shape and equatorial/polar gravity. No terrain, tide, latitude datum or measured anomaly correction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=somigliana-normal-gravity-reference) · [Technical reference](https://geoscienceaustralia.github.io/galileoQC/tutorials/Gravimeter_Corrections.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "latitudeDegrees": 0,
      "equatorialGravity": 9.8,
      "polarGravity": 9.9,
      "semimajor": 2,
      "semiminor": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gravity": 9.8
}
```

## Astrogeodetic Deflection Laplace Correction

Service ID: `astrogeodetic-deflection-laplace-correction`. USD 1.00 per job.

Apply first-order north/east deflection components to astronomical coordinates and the NGS horizontal-line Laplace azimuth sign convention. No deflection grid, steep-sight correction or datum certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=astrogeodetic-deflection-laplace-correction) · [Technical reference](https://www.ngs.noaa.gov/GEOID/signs.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "geodeticLatitudeDegrees": 45,
      "geodeticLongitudeDegrees": 0,
      "xiArcseconds": 1,
      "etaArcseconds": 1,
      "astronomicAzimuthDegrees": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/astronomicLatitudeDegrees": 45.000277777777775,
  "/records/0/astronomicLongitudeDegrees": 0.0003928371006591931,
  "/records/0/laplaceAzimuthDegrees": 0.0002777777777777778
}
```

## Minor Great Circle Route Latitude Extrema

Service ID: `minor-great-circle-route-latitude-extrema`. USD 1.00 per job.

Find exact latitude extrema along a distinct nonantipodal minor great-circle arc by testing its pole-projection vertices for membership. No waypoint interpolation or quaternion SLERP is performed. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=minor-great-circle-route-latitude-extrema) · [Technical reference](https://edwilliams.org/avform.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "startLatitudeDegrees": 45,
      "startLongitudeDegrees": -90,
      "endLatitudeDegrees": 45,
      "endLongitudeDegrees": 90
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/maximumLatitudeDegrees": 90,
  "/records/0/minimumLatitudeDegrees": 45
}
```

## Fractional Aperture Background Photometry

Service ID: `fractional-aperture-background-photometry`. USD 1.00 per job.

Sum supplied fractional aperture pixel weights with a common estimated background and its correlated variance. Pixel variance follows fractional-area convention; weights do not encode a noise resampling kernel. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fractional-aperture-background-photometry) · [Technical reference](https://photutils.readthedocs.io/en/stable/user_guide/aperture.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pixels": [
        {
          "value": 10,
          "variance": 4,
          "weight": 1
        },
        {
          "value": 6,
          "variance": 1,
          "weight": 0.5
        }
      ],
      "background": 2,
      "backgroundVariance": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/flux": 10,
  "/records/0/variance": 6.75,
  "/records/0/areaPixels": 1.5
}
```

## Moffat Point Spread Encircled Energy

Service ID: `moffat-point-spread-encircled-energy`. USD 1.00 per job.

Integrate a normalized circular Moffat PSF into encircled-energy fractions and analytic FWHM. No PSF fitting, diffraction model or aperture calibration is inferred. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=moffat-point-spread-encircled-energy) · [Technical reference](https://photutils.readthedocs.io/en/stable/api/photutils.psf.MoffatPSF.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "alphaPixels": 1,
      "beta": 2,
      "radiiPixels": [
        0,
        1,
        3
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/fractions": [
    0,
    0.5,
    0.9
  ],
  "/records/0/fwhmPixels": 1.2871885058111654
}
```

## Background Subtracted Stellar Image Moments

Service ID: `background-subtracted-stellar-image-moments`. USD 1.00 per job.

Calculate nonnegative background-subtracted image centroid and central second moments. Signed residual images, PSF fitting and astrophysical source classification are excluded. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=background-subtracted-stellar-image-moments) · [Technical reference](https://photutils.readthedocs.io/en/stable/api/photutils.centroids.centroid_com.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pixels": [
        {
          "x": -1,
          "y": 0,
          "signal": 1
        },
        {
          "x": 1,
          "y": 0,
          "signal": 1
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/flux": 2,
  "/records/0/centroidX": 0,
  "/records/0/centroidY": 0,
  "/records/0/momentXX": 1,
  "/records/0/momentYY": 0,
  "/records/0/momentXY": 0
}
```

## Ccd Source Noise Exposure Solution

Service ID: `ccd-source-noise-exposure-solution`. USD 1.00 per job.

Solve the Poisson source/sky/dark plus one-read CCD exposure equation for a supplied target signal-to-noise ratio. No detector acquisition, saturation guarantee or correlated-noise model. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ccd-source-noise-exposure-solution) · [Technical reference](https://hst-docs.stsci.edu/acsihb/chapter-9-exposure-time-calculations/9-3-computing-exposure-times)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sourceElectronsSecond": 1,
      "skyElectronsPixelSecond": 0,
      "darkElectronsPixelSecond": 0,
      "pixels": 1,
      "readNoiseElectrons": 0,
      "targetSnr": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/seconds": 100,
  "/records/0/sourceElectrons": 100,
  "/records/0/varianceElectronsSquared": 100,
  "/records/0/achievedSnr": 10
}
```

## Ab St Spectral Density Magnitude Pair

Service ID: `ab-st-spectral-density-magnitude-pair`. USD 1.00 per job.

Convert one monochromatic spectral density between f-nu and f-lambda and report conventional AB and ST magnitudes. Wavelength is Angstrom; no finite-passband colour correction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ab-st-spectral-density-magnitude-pair) · [Technical reference](https://www.stsci.edu/hst/instrumentation/acs/data-analysis/zeropoints)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "wavelengthAngstrom": 5475.330656681841,
      "fnuErgSecondCm2Hz": 1e-20
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/abMagnitude": 1.4,
  "/records/0/stMagnitude": 1.4
}
```

## Flux Conserving Spectral Bin Overlap

Service ID: `flux-conserving-spectral-bin-overlap`. USD 1.00 per job.

Rebin piecewise-constant astronomical spectral density by exact wavelength-bin overlap. No interpolation beyond source coverage, instrument response or frequency/wavelength mixing. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=flux-conserving-spectral-bin-overlap) · [Technical reference](https://specutils.readthedocs.io/en/stable/manipulation.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sourceEdges": [
        1,
        2,
        4
      ],
      "sourceDensity": [
        2,
        4
      ],
      "targetEdges": [
        1,
        3,
        4
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/targetDensity": [
    3,
    4
  ],
  "/records/0/integratedFlux": 10
}
```

## Continuum Normalized Line Equivalent Width

Service ID: `continuum-normalized-line-equivalent-width`. USD 1.00 per job.

Integrate supplied continuum-normalized spectral line equivalent width by trapezoids and transform wavelength width to rest frame. Emission widths may be negative; no continuum fit or line identification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=continuum-normalized-line-equivalent-width) · [Technical reference](https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Stellar_Atmospheres_(Tatum)/11:_Curve_of_Growth/11.03:_Theory_of_the_Curve_of_Growth)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "wavelengths": [
        1,
        2,
        3
      ],
      "flux": [
        1,
        0,
        1
      ],
      "continuum": [
        1,
        1,
        1
      ],
      "redshift": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/observedEquivalentWidth": 1,
  "/records/0/restEquivalentWidth": 0.5
}
```

## Circular Exoplanet Transit Contact Duration

Service ID: `circular-exoplanet-transit-contact-duration`. USD 1.00 per job.

Calculate first-to-fourth and second-to-third contact durations of a circular orbit across a spherical star. Impact is in stellar radii; grazing events have zero full-transit duration. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=circular-exoplanet-transit-contact-duration) · [Technical reference](https://arxiv.org/html/1001.2010)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "periodDays": 6,
      "axisOverStarRadius": 2,
      "radiusRatio": 1,
      "impact": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/totalDays": 3,
  "/records/0/fullDays": 0
}
```

## Eccentric Radial Velocity Curve

Service ID: `eccentric-radial-velocity-curve`. USD 1.00 per job.

Evaluate a supplied single-companion Keplerian radial-velocity model at supplied true anomalies. No anomaly/time solver, mass inference or planet detection. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=eccentric-radial-velocity-curve) · [Technical reference](https://gerbil.phys.uvic.ca/~tatum/celmechs/celm18.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "semiAmplitude": 10,
      "eccentricity": 0.5,
      "argumentDegrees": 0,
      "systemicVelocity": 2,
      "trueAnomaliesDegrees": [
        0,
        180
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/velocities": [
    17,
    -3
  ]
}
```

## Point Lens Microlensing Lightcurve

Service ID: `point-lens-microlensing-lightcurve`. USD 1.00 per job.

Evaluate a rectilinear point-source point-lens microlensing light curve with a positive minimum impact parameter. Stable amplification excess avoids subtracting large terms; no finite source, blending or parallax. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=point-lens-microlensing-lightcurve) · [Technical reference](https://arxiv.org/html/astro-ph/9606001)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "minimumImpact": 1,
      "einsteinTime": 1,
      "peakTime": 0,
      "times": [
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/amplifications": [
    1.3416407864998738
  ],
  "/records/0/separations": [
    1
  ]
}
```

## Relativistic Bipolar Jet Apparent Motion

Service ID: `relativistic-bipolar-jet-apparent-motion`. USD 1.00 per job.

Evaluate apparent transverse speeds and Doppler factors for symmetric ballistic relativistic jets. No distance inference, beaming spectral index or fitted source interpretation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=relativistic-bipolar-jet-apparent-motion) · [Technical reference](https://ned.ipac.caltech.edu/level5/Urry1/UrryP_appena.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "beta": 0.8,
      "inclinationDegrees": 90
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/approachingBetaApp": 0.8,
  "/records/0/recedingBetaApp": 0.8,
  "/records/0/dopplerApproach": 0.6,
  "/records/0/dopplerRecede": 0.6
}
```

## Quadratic Stellar Limb Darkening Profile

Service ID: `quadratic-stellar-limb-darkening-profile`. USD 1.00 per job.

Evaluate a quadratic stellar limb-darkening law and exact disk-average intensity while rejecting negative intensity anywhere on the disk. No atmosphere fitting or transit occultation integration. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=quadratic-stellar-limb-darkening-profile) · [Technical reference](https://arxiv.org/html/1001.2010)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "u1": 1,
      "u2": 0,
      "radii": [
        0,
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/intensities": [
    1,
    0
  ],
  "/records/0/diskMeanIntensity": 0.6666666666666666
}
```

## Single Lined Binary Companion Mass Root

Service ID: `single-lined-binary-companion-mass-root`. USD 1.00 per job.

Invert a supplied single-lined spectroscopic mass function for companion mass at explicit primary mass and inclination. No inclination inference, classification or posterior interval. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=single-lined-binary-companion-mass-root) · [Technical reference](https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_%28Tatum%29/18%3A_Spectroscopic_Binary_Stars/18.04%3A_Masses)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "massFunction": 0.25,
      "primaryMass": 1,
      "inclinationDegrees": 90
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/companionMass": 1,
  "/records/0/predictedMassFunction": 0.25
}
```

## Central Quadratic Limb Transit Integral

Service ID: `central-quadratic-limb-transit-integral`. USD 1.00 per job.

Analytically integrate a central opaque transit across a quadratic limb-darkened stellar disk. This solves intensity-weighted blocked flux rather than uniform circle overlap; off-centre geometry is excluded. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=central-quadratic-limb-transit-integral) · [Technical reference](https://arxiv.org/html/1001.2010)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "radiusRatio": 0.5,
      "u1": 1,
      "u2": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/relativeFlux": 0.649519052838329,
  "/records/0/blockedFraction": 0.350480947161671
}
```

## Hyperbolic Gravity Assist Turn Geometry

Service ID: `hyperbolic-gravity-assist-turn-geometry`. USD 1.00 per job.

Evaluate a point-mass unpowered hyperbolic flyby from explicit hyperbolic excess and periapsis. No atmosphere, collision assessment, spacecraft navigation or ephemeris. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=hyperbolic-gravity-assist-turn-geometry) · [Technical reference](https://orbital-mechanics.space/the-orbit-equation/hyperbolic-trajectories.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "mu": 1,
      "periapsisRadius": 1,
      "excessSpeed": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/eccentricity": 2,
  "/records/0/turnDegrees": 60,
  "/records/0/periapsisSpeed": 1.7320508075688772,
  "/records/0/impactParameter": 1.7320508075688772
}
```

## Ideal Multistage Rocket Mass Accounting

Service ID: `ideal-multistage-rocket-mass-accounting`. USD 1.00 per job.

Reconcile ideal serial rocket staging with each spent dry stage discarded, ordered first-to-last fired. Uses effective exhaust speed; no gravity/drag losses, design approval or launch control. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ideal-multistage-rocket-mass-accounting) · [Technical reference](https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/ideal-rocket-equation/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "payloadMass": 1,
      "stages": [
        {
          "dryMass": 1,
          "propellantMass": 2,
          "exhaustSpeed": 1
        },
        {
          "dryMass": 1,
          "propellantMass": 2,
          "exhaustSpeed": 1
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/initialMass": 7,
  "/records/0/finalMass": 1,
  "/records/0/deltaV": 1.0296194171811581
}
```

## Restricted Three Body Jacobi State

Service ID: `restricted-three-body-jacobi-state`. USD 1.00 per job.

Evaluate dimensionless circular restricted three-body effective potential and Jacobi constant in the rotating barycentric frame. No trajectory propagation, stability or mission clearance. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=restricted-three-body-jacobi-state) · [Technical reference](https://orbital-mechanics.space/the-n-body-problem/lagrange-points.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "massFraction": 0.5,
      "position": [
        0,
        0,
        0
      ],
      "velocity": [
        0,
        0,
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/jacobiConstant": 4,
  "/records/0/effectivePotential": 2
}
```

## Collinear Lagrange Point Roots

Service ID: `collinear-lagrange-point-roots`. USD 1.00 per job.

Solve all three collinear circular restricted three-body equilibrium coordinates in canonical units by bounded bisection. No halo orbit or operational stationkeeping. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=collinear-lagrange-point-roots) · [Technical reference](https://orbital-mechanics.space/the-n-body-problem/lagrange-points.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "massFraction": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/l1": 0
}
```

## Ideal Solar Sail Pressure Vector

Service ID: `ideal-solar-sail-pressure-vector`. USD 1.00 per job.

Calculate ideal specular flat-sail force along the supplied unit normal at a declared incident flux. Unit sun direction points with incident momentum; no thermal, diffuse or spacecraft control model. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ideal-solar-sail-pressure-vector) · [Technical reference](https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Dissertations/2011_Wawrzyniak.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "irradiance": 10,
      "area": 2,
      "normal": [
        1,
        0,
        0
      ],
      "sunDirection": [
        1,
        0,
        0
      ],
      "lightSpeed": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/force": [
    4,
    0,
    0
  ],
  "/records/0/incidenceCosine": 1
}
```

## Finite Sun Umbra Penumbra Cone

Service ID: `finite-sun-umbra-penumbra-cone`. USD 1.00 per job.

Evaluate axial straight-ray small-angle shadow-cone cross sections behind a spherical occluder. Antumbra, observer flux and finite-distance exact tangent geometry are excluded. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-sun-umbra-penumbra-cone) · [Technical reference](https://science.nasa.gov/eclipses/geometry/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sunRadius": 2,
      "occluderRadius": 1,
      "separation": 10,
      "distanceBehind": 5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/umbraRadius": 0.5,
  "/records/0/penumbraRadius": 2.5,
  "/records/0/umbraLength": 10
}
```

## Two Body Lagrange Fg Universal Step

Service ID: `two-body-lagrange-fg-universal-step`. USD 1.00 per job.

Propagate one bounded two-body state with universal variables and Lagrange f,g coefficients. Central collision and nonconvergent steps reject; no perturbations, ephemeris or guidance. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-body-lagrange-fg-universal-step) · [Technical reference](https://orbital-mechanics.space/time-since-periapsis-and-keplers-equation/universal-variables.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "mu": 1,
      "position": [
        1,
        0,
        0
      ],
      "velocity": [
        0,
        1,
        0
      ],
      "elapsed": 1.5707963267948966
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/position": [
    0,
    1,
    0
  ],
  "/records/0/velocity": [
    -1,
    0,
    0
  ],
  "/records/0/radius": 1
}
```

## Spherical Subpoint Ground Track

Service ID: `spherical-subpoint-ground-track`. USD 1.00 per job.

Rotate supplied inertial position directions into spherical geocentric subpoints with separately supplied Earth rotation angles. No orbital ephemeris, geodetic latitude, terrain or pass prediction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=spherical-subpoint-ground-track) · [Technical reference](https://gssc.esa.int/navipedia/index.php?title=Transformation_between_Celestial_and_Terrestrial_Frames)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "inertialPositions": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ]
      ],
      "rotationAnglesDegrees": [
        0,
        90
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/latitudesDegrees": [
    0,
    0
  ],
  "/records/0/longitudesDegrees": [
    0,
    0
  ]
}
```

## Two Impulse Circular Orbit Plane Change

Service ID: `two-impulse-circular-orbit-plane-change`. USD 1.00 per job.

Evaluate a user-chosen split of orbital plane change between two circular-transfer impulses and perform a bounded coarse-search/refinement over the split fraction. Node selection, perturbations and operational maneuver commands are excluded; reported minimum is numerical within the supplied two-burn model. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-impulse-circular-orbit-plane-change) · [Technical reference](https://orbital-mechanics.space/orbital-maneuvers/plane-change-maneuvers.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "mu": 1,
      "firstRadius": 1,
      "secondRadius": 1,
      "inclinationChangeDegrees": 60,
      "firstBurnShare": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/firstDeltaV": 0,
  "/records/0/secondDeltaV": 1,
  "/records/0/totalDeltaV": 1
}
```

## Peters Binary Orbit Secular Decay

Service ID: `peters-binary-orbit-secular-decay`. USD 1.00 per job.

Evaluate orbit-averaged Peters quadrupole semimajor-axis and eccentricity loss rates of an isolated point-mass binary. No strong-field waveform or merger forecast. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=peters-binary-orbit-secular-decay) · [Technical reference](https://legwork.readthedocs.io/en/latest/notebooks/Derivations.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "massA": 1,
      "massB": 1,
      "semimajor": 1,
      "eccentricity": 0,
      "gravityConstant": 1,
      "lightSpeed": 20
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/axisRate": -0.000008,
  "/records/0/eccentricityRate": 0
}
```

## Gibbs Three Position Orbit Velocity

Service ID: `gibbs-three-position-orbit-velocity`. USD 1.00 per job.

Infer the middle Keplerian velocity from three ordered nonzero coplanar position vectors by Gibbs orbit determination, retaining specific energy and angular momentum. No observation times, covariance fit, short-arc robustness or real-object orbit validation. Degenerate and inconsistent vector geometry rejects. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=gibbs-three-position-orbit-velocity) · [Technical reference](https://kyleniemeyer.github.io/space-systems-notes/orbital-mechanics/orbits-space.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "mu": 1,
      "positions": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          -1,
          0,
          0
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/middleVelocity": [
    -1,
    0,
    0
  ],
  "/records/0/specificEnergy": -0.5,
  "/records/0/angularMomentum": [
    0,
    0,
    1
  ]
}
```

## Lambert Short Way Zero Revolution Boundary Solver

Service ID: `lambert-short-way-zero-revolution-boundary-solver`. USD 1.00 per job.

Solve the short-way zero-revolution Lambert two-position/time boundary problem with a bounded universal-variable bracket and Stumpff functions. The vector cross product fixes traversal orientation; collinear positions and unsupported time brackets reject. No multi-revolution branch, maneuver authorization or real trajectory validation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lambert-short-way-zero-revolution-boundary-solver) · [Technical reference](https://kyleniemeyer.github.io/space-systems-notes/orbital-mechanics/orbits-space.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "mu": 1,
      "initialPosition": [
        1,
        0,
        0
      ],
      "finalPosition": [
        0,
        1,
        0
      ],
      "flightTime": 1.5707963267948966
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/initialVelocity": [
    0,
    1,
    0
  ],
  "/records/0/finalVelocity": [
    -1,
    0,
    0
  ],
  "/records/0/universalParameter": 2.4674011002723395,
  "/records/0/timeResidual": 0
}
```

## Flrw Distance Lookback Quadrature

Service ID: `flrw-distance-lookback-quadrature`. USD 1.00 per job.

Integrate matter, curvature and cosmological-constant FLRW distances and lookback time with Simpson quadrature starting at 512 panels with bounded refinement. No radiation, fitted cosmology or observational distance guarantee. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=flrw-distance-lookback-quadrature) · [Technical reference](https://arxiv.org/html/astro-ph/9905116v4)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "redshift": 1,
      "matter": 0,
      "lambda": 0,
      "hubble": 1,
      "lightSpeed": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/radialDistance": 0.6931471805599453,
  "/records/0/angularDistance": 0.375,
  "/records/0/luminosityDistance": 1.5,
  "/records/0/lookbackTime": 0.5
}
```

## Point Mass Einstein Ring Geometry

Service ID: `point-mass-einstein-ring-geometry`. USD 1.00 per job.

Compute the thin point-mass lens Einstein angle from explicit angular-diameter distances. Distances need not add in cosmology; no mass fitting, strong-field or image identification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=point-mass-einstein-ring-geometry) · [Technical reference](https://arxiv.org/html/astro-ph/9606001)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lensMass": 1,
      "observerLensDistance": 1,
      "observerSourceDistance": 2,
      "lensSourceDistance": 1,
      "gravityConstant": 1,
      "lightSpeed": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/einsteinRadians": 0.7071067811865476,
  "/records/0/lensPlaneRadius": 0.7071067811865476
}
```

## Singular Isothermal Sphere Lens Images

Service ID: `singular-isothermal-sphere-lens-images`. USD 1.00 per job.

Solve the one-dimensional circular singular isothermal sphere lens equation away from exact alignment. Negative magnification denotes odd parity; no external shear or real-lens fit. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=singular-isothermal-sphere-lens-images) · [Technical reference](https://arxiv.org/html/astro-ph/9606001)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "einsteinAngle": 1,
      "sourceOffset": 0.5
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/positions": [
    1.5,
    -0.5
  ],
  "/records/0/signedMagnifications": [
    3,
    -1
  ],
  "/records/0/totalMagnification": 4
}
```

## Schechter Luminosity Bin Integrals

Service ID: `schechter-luminosity-bin-integrals`. USD 1.00 per job.

Integrate a supplied Schechter luminosity function over strictly positive finite bins. No extrapolation to zero luminosity, population fit or observed number-density claim. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=schechter-luminosity-bin-integrals) · [Technical reference](https://docs.astropy.org/en/stable/api/astropy.modeling.powerlaws.Schechter1D.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "normalization": 1,
      "characteristicLuminosity": 1,
      "alpha": 0,
      "binEdges": [
        1,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/numberDensities": [
    0.23254415793482963
  ]
}
```

## Theis Confined Well Drawdown History

Service ID: `theis-confined-well-drawdown-history`. USD 1.00 per job.

Evaluate the Theis solution for a fully penetrating constant-rate well in an infinite homogeneous isotropic confined aquifer. No parameter estimation or well operation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=theis-confined-well-drawdown-history) · [Technical reference](https://interactive-education.gw-project.org/analytical-groundwater-modeling/chap9/9.1_theis_well.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "rate": 12.566370614359172,
      "transmissivity": 1,
      "storativity": 1,
      "radius": 2,
      "times": [
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/drawdowns": [
    0.21938393439552026
  ],
  "/records/0/uValues": [
    1
  ]
}
```

## Dupuit Recharge Water Table Profile

Service ID: `dupuit-recharge-water-table-profile`. USD 1.00 per job.

Solve steady unconfined Dupuit flow between fixed-head boundaries over a horizontal base with uniform recharge. Heads are saturated thickness; no seepage face or layered calibration. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dupuit-recharge-water-table-profile) · [Technical reference](https://interactive-education.gw-project.org/analytical-groundwater-modeling/chap1/1.2_recharge_between_two_rivers.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "conductivity": 1,
      "length": 2,
      "leftHead": 1,
      "rightHead": 1,
      "recharge": 1,
      "positions": [
        0,
        1,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/heads": [
    1,
    1.4142135623730951,
    1
  ],
  "/records/0/unitDischarges": [
    -1,
    0,
    1
  ]
}
```

## Hantush Leaky Aquifer Well Integral

Service ID: `hantush-leaky-aquifer-well-integral`. USD 1.00 per job.

Integrate the Hantush leaky-well function with negligible aquitard storage over a bounded dimensionless profile. Log integration handles small u; no leakage parameter fitting. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=hantush-leaky-aquifer-well-integral) · [Technical reference](https://books.gw-project.org/an-introduction-to-hydraulic-testing-in-hydrogeology/chapter/hantush%E2%80%91jacob-solution-leaky-confined%E2%80%91no-water-released-from-aquitard-storage/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "rate": 12.566370614359172,
      "transmissivity": 1,
      "u": 1,
      "radiusOverLeakageLength": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/wellFunction": 0.21938393439552026,
  "/records/0/drawdown": 0.21938393439552026
}
```

## Uniform Flow Pumping Capture Boundary

Service ID: `uniform-flow-pumping-capture-boundary`. USD 1.00 per job.

Parameterize one half of the ideal two-dimensional pumping-well capture dividing streamline in uniform confined flow. Well is at origin; x=stagnationDistance at the downstream limit. No real capture delineation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=uniform-flow-pumping-capture-boundary) · [Technical reference](https://interactive-education.gw-project.org/analytical-groundwater-modeling/chap7/7.2_capture_zones.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "rate": 6.283185307179586,
      "backgroundDarcyFlux": 1,
      "thickness": 1,
      "anglesDegrees": [
        90
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/stagnationDistance": 1,
  "/records/0/captureWidth": 6.283185307179586,
  "/records/0/x": [
    0
  ],
  "/records/0/y": [
    1.5707963267948966
  ]
}
```

## Hvorslev Slug Decay Conductivity

Service ID: `hvorslev-slug-decay-conductivity`. USD 1.00 per job.

Reduce two positive monotone slug recovery observations using the stated long-screen Hvorslev shape approximation. No well storage correction, automated test selection or aquifer certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=hvorslev-slug-decay-conductivity) · [Technical reference](https://books.gw-project.org/an-introduction-to-hydraulic-testing-in-hydrogeology/chapter/methods-to-interpret-overdamped-slug-tests/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "casingRadius": 1,
      "screenRadius": 1,
      "screenLength": 20.085536923187668,
      "timeA": 0,
      "timeB": 1,
      "headA": 2.718281828459045,
      "headB": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/timeConstant": 1,
  "/records/0/conductivity": 0.07468060255179591
}
```

## Ogata Banks Step Solute Breakthrough

Service ID: `ogata-banks-step-solute-breakthrough`. USD 1.00 per job.

Evaluate the semi-infinite Ogata-Banks step-input advection-dispersion solution using stable complementary-error-function scaling. No reaction, sorption, parameter fitting or drinking-water determination. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ogata-banks-step-solute-breakthrough) · [Technical reference](https://www.opengeosys.org/stable/docs/benchmarks/hydro-thermal/classicaltransportexample_isotropic_diffusion_stb/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "velocity": 1,
      "dispersion": 1,
      "distance": 0,
      "times": [
        1,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/concentrationFractions": [
    1,
    1
  ]
}
```

## Van Genuchten Mualem Retention Profile

Service ID: `van-genuchten-mualem-retention-profile`. USD 1.00 per job.

Evaluate van Genuchten retention with Mualem relative conductivity from explicit parameters. Assumes m=1-1/n, drying suction magnitude and homogeneous equilibrium; no fitted soil or irrigation advice. This source-bound profile fixes poreConnectivity at0.5; other connectivity exponents are excluded. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=van-genuchten-mualem-retention-profile) · [Technical reference](https://pflotran.org/documentation-release/theory_guide/constitutive_relations.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "residualWater": 0.1,
      "saturatedWater": 0.5,
      "alpha": 1,
      "n": 2,
      "poreConnectivity": 0.5,
      "saturatedConductivity": 1,
      "suctions": [
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/waterContents": [
    0.5
  ],
  "/records/0/conductivities": [
    1
  ],
  "/records/0/effectiveSaturations": [
    1
  ]
}
```

## Stratified Aquifer Conductivity Tensor

Service ID: `stratified-aquifer-conductivity-tensor`. USD 1.00 per job.

Homogenize parallel planar isotropic layers into exact parallel arithmetic and perpendicular harmonic conductivity. No crossflow, inclined interfaces or calibrated regional tensor. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=stratified-aquifer-conductivity-tensor) · [Technical reference](https://modflow6.readthedocs.io/en/latest/_mf6io/gwf-npf.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "layers": [
        {
          "thickness": 1,
          "conductivity": 1
        },
        {
          "thickness": 1,
          "conductivity": 3
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/parallelConductivity": 2,
  "/records/0/perpendicularConductivity": 1.5,
  "/records/0/thickness": 2,
  "/records/0/anisotropyRatio": 1.3333333333333333
}
```

## Exponential Groundwater Age Tracer Mixture

Service ID: `exponential-groundwater-age-tracer-mixture`. USD 1.00 per job.

Integrate an exponential groundwater age distribution into age-bin fractions and a steady decaying-tracer mixture. Constant historical input and first-order decay are explicit; no actual residence-age inference. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=exponential-groundwater-age-tracer-mixture) · [Technical reference](https://gnssn.iaea.org/main/ncp/Tunisia/lrae/documents/tracers/Volume_VI.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "meanAge": 1,
      "decayRate": 1,
      "inputConcentration": 2,
      "ageEdges": [
        0,
        1,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/mixtureConcentration": 1,
  "/records/0/ageFractions": [
    0.6321205588285577,
    0.23254415793482963
  ]
}
```

## Confined Aquifer Explicit Head Grid Step

Service ID: `confined-aquifer-explicit-head-grid-step`. USD 1.00 per job.

Advance one constant-diffusivity confined aquifer finite-difference step with fixed edge heads and uniform recharge head rate. Stability is checked before computation; no boundary fitting or operational groundwater prediction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=confined-aquifer-explicit-head-grid-step) · [Technical reference](https://modflow6.readthedocs.io/en/latest/_mf6io/gwf-npf.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "heads": [
        [
          0,
          0,
          0
        ],
        [
          0,
          4,
          0
        ],
        [
          0,
          0,
          0
        ]
      ],
      "diffusivity": 1,
      "cellSize": 1,
      "stepTime": 0.25,
      "rechargeHeadRate": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/heads": [
    [
      0,
      0,
      0
    ],
    [
      0,
      0,
      0
    ],
    [
      0,
      0,
      0
    ]
  ],
  "/records/0/maximumChange": 4
}
```

## Philip Two Term Rainfall Ponding

Service ID: `philip-two-term-rainfall-ponding`. USD 1.00 per job.

Integrate rainfall capped by the stated Philip clock-time capacity S/(2 sqrt(t)) plus K, splitting at exact ponding time. This profile deliberately does not shift equivalent infiltration time after ponding. pondingTime is the declared clock-time capacity crossing, not a time-compressed physical ponding estimate. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=philip-two-term-rainfall-ponding) · [Technical reference](https://hess.copernicus.org/articles/10/861/2006/hess-10-861-2006.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "sorptivity": 2,
      "conductivity": 0,
      "rainIntensity": 1,
      "duration": 4
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/pondingTime": 1,
  "/records/0/infiltration": 3,
  "/records/0/rainfallExcess": 1
}
```

## Airy Finite Depth Wave Dispersion

Service ID: `airy-finite-depth-wave-dispersion`. USD 1.00 per job.

Solve the finite-depth linear surface-gravity-wave dispersion relation and group speed. No currents, breaking, capillarity or sea-state prediction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=airy-finite-depth-wave-dispersion) · [Technical reference](https://ocw.mit.edu/courses/2-016-hydrodynamics-13-012-fall-2005/8f21a5cde79c7f8bd8dc435d5b6e902b_2005reading7.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "period": 7.1997607828454475,
      "depth": 1,
      "gravity": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/wavenumber": 1,
  "/records/0/wavelength": 6.283185307179586,
  "/records/0/phaseSpeed": 0.8726936208978296
}
```

## Second Order Stokes Surface Profile

Service ID: `second-order-stokes-surface-profile`. USD 1.00 per job.

Evaluate the finite-depth second-order Stokes free-surface elevation for a declared small-steepness wave. Mean level is zero in this profile; no breaking or structural-load design. The second harmonic must not exceed 10 percent of the fundamental; this is a declared conservative numerical model profile, not physical validation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=second-order-stokes-surface-profile) · [Technical reference](https://coastalwiki.org/wiki/Shallow-water_wave_theory)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "amplitude": 0.1,
      "wavenumber": 1,
      "depth": 10,
      "phasesDegrees": [
        90
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/elevations": [
    -0.0050000000824461455
  ]
}
```

## Linear Wave Shoaling Refraction Transect

Service ID: `linear-wave-shoaling-refraction-transect`. USD 1.00 per job.

Conserve linear-wave cross-shore energy flux across parallel depth contours with Snell refraction. No reflection, dissipation, current, breaking or coastal safety result. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=linear-wave-shoaling-refraction-transect) · [Technical reference](https://coastalwiki.org/wiki/Shallow-water_wave_theory)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "period": 6.283185307179586,
      "offshoreHeight": 2,
      "offshoreAngleDegrees": 0,
      "depths": [
        10,
        10
      ],
      "gravity": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/heights": [
    2,
    2
  ],
  "/records/0/anglesDegrees": [
    0,
    0
  ]
}
```

## Airy Wave Depth Orbital Kinematics

Service ID: `airy-wave-depth-orbital-kinematics`. USD 1.00 per job.

Evaluate linear-wave horizontal and vertical particle velocities from seabed to mean surface at a supplied phase. No stretching above mean surface or real wave loads. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=airy-wave-depth-orbital-kinematics) · [Technical reference](https://ocw.mit.edu/courses/2-016-hydrodynamics-13-012-fall-2005/8f21a5cde79c7f8bd8dc435d5b6e902b_2005reading7.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "amplitude": 1,
      "period": 7.1997607828454475,
      "depth": 1,
      "elevations": [
        -1,
        0
      ],
      "phaseDegrees": 90,
      "gravity": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/verticalVelocities": [
    0,
    0.8726936208978296
  ]
}
```

## Directional Wave Radiation Stress Tensor

Service ID: `directional-wave-radiation-stress-tensor`. USD 1.00 per job.

Sum the linear-wave horizontal radiation-stress tensor for incoherent directional energy components and supplied group/phase ratios. No wave setup solver or shoreline prediction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=directional-wave-radiation-stress-tensor) · [Technical reference](https://github.com/NOAA-EMC/WW3/blob/develop/manual/eqs/output.tex)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "components": [
        {
          "energy": 2,
          "directionDegrees": 0,
          "groupRatio": 1
        },
        {
          "energy": 2,
          "directionDegrees": 90,
          "groupRatio": 1
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/sxx": 4,
  "/records/0/syy": 4,
  "/records/0/sxy": 0,
  "/records/0/totalEnergy": 4
}
```

## Tidal Constituent Nodal Harmonic Synthesis

Service ID: `tidal-constituent-nodal-harmonic-synthesis`. USD 1.00 per job.

Synthesize a declared fixed-constituent harmonic tide with supplied datum, phase epoch and fixed nodal corrections. No astronomical coefficient lookup, station prediction certification or navigation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=tidal-constituent-nodal-harmonic-synthesis) · [Technical reference](https://mcirano.ufba.br/ftp/books/stewart05/book.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "datum": 1,
      "timesHours": [
        0,
        1
      ],
      "constituents": [
        {
          "amplitude": 2,
          "speedDegreesHour": 90,
          "phaseDegrees": 0,
          "nodalFactor": 1,
          "nodalCorrectionDegrees": 0
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/heights": [
    3,
    1
  ]
}
```

## Constant Viscosity Ekman Spiral

Service ID: `constant-viscosity-ekman-spiral`. USD 1.00 per job.

Evaluate the infinite-depth constant-viscosity Ekman spiral with depths positive downward. Surface stress, density and signed Coriolis are supplied; no bottom boundary or current prediction. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=constant-viscosity-ekman-spiral) · [Technical reference](https://mcirano.ufba.br/ftp/books/stewart05/book.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "windStressEast": 1,
      "windStressNorth": 0,
      "density": 1,
      "eddyViscosity": 1,
      "coriolis": 0.02,
      "depths": [
        0
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/eastVelocities": [
    5
  ],
  "/records/0/northVelocities": [
    -5
  ],
  "/records/0/transportEast": 0,
  "/records/0/transportNorth": -50
}
```

## Ocean Thermal Wind Layer Shear

Service ID: `ocean-thermal-wind-layer-shear`. USD 1.00 per job.

Integrate hydrostatic geostrophic thermal-wind shear through a constant horizontal density-gradient layer. Difference is upper minus lower velocity; no barotropic reference or observed current validation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ocean-thermal-wind-layer-shear) · [Technical reference](https://mcirano.ufba.br/ftp/books/stewart05/book.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "densityEastGradient": 1,
      "densityNorthGradient": 2,
      "referenceDensity": 1,
      "coriolis": 1,
      "gravity": 1,
      "thickness": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/eastVelocityDifference": 4,
  "/records/0/northVelocityDifference": -2
}
```

## Two Layer Long Wave Mode Speeds

Service ID: `two-layer-long-wave-mode-speeds`. USD 1.00 per job.

Solve the two-layer inviscid free-surface long-wave quadratic for external and internal mode speeds using stable small-root algebra. No rotation, shear or breaking. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-layer-long-wave-mode-speeds) · [Technical reference](https://mcirano.ufba.br/ftp/books/stewart05/book.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "upperDepth": 1,
      "lowerDepth": 1,
      "upperDensity": 1,
      "lowerDensity": 4,
      "gravity": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/externalSpeed": 1.224744871391589,
  "/records/0/internalSpeed": 0.7071067811865476
}
```

## Estuary Two Box Steady Salinity

Service ID: `estuary-two-box-steady-salinity`. USD 1.00 per job.

Solve a steady two-box salt balance with freshwater entering the inner box, outward river advection and symmetric exchanges between boxes and ocean. No estuarine calibration, stratification or water-quality compliance. River salt advected from the inner box enters the outer box explicitly. Both salt-budget residuals and ocean export are retained. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=estuary-two-box-steady-salinity) · [Technical reference](https://mcirano.ufba.br/ftp/books/stewart05/book.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "riverFlow": 1,
      "exchangeInner": 1,
      "exchangeOcean": 1,
      "oceanSalinity": 30
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/innerSalinity": 7.5,
  "/records/0/outerSalinity": 15,
  "/records/0/oceanSaltInput": 15,
  "/records/0/oceanSaltExport": 15,
  "/records/0/innerSaltResidual": 0,
  "/records/0/outerSaltResidual": 0
}
```

## Unesco Eos80 Surface Seawater Density

Service ID: `unesco-eos80-surface-seawater-density`. USD 1.00 per job.

Evaluate the UNESCO EOS-80 atmospheric-pressure seawater density polynomial using practical salinity and IPTS-68 temperature input. No TEOS-10 conversion, pressure correction or ocean-state validation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=unesco-eos80-surface-seawater-density) · [Technical reference](https://pythonhosted.org/seawater/eos80.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "temperatureC": 0,
      "practicalSalinity": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/densityKgM3": 999.842594
}
```

## Annular Terrain Column Gravity Correction

Service ID: `annular-terrain-column-gravity-correction`. USD 1.00 per job.

Sum exact axial gravity of full annular terrain columns with explicit positive-down depths and density contrasts. Stable root differences avoid cancellation; no terrain grid fetching or gravity reduction certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=annular-terrain-column-gravity-correction) · [Technical reference](https://farside.ph.utexas.edu/teaching/355/Surveyhtml/node50.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gravityConstant": 1,
      "columns": [
        {
          "innerRadius": 0,
          "outerRadius": 1,
          "topDepth": 0,
          "bottomDepth": 1,
          "densityContrast": 1
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/verticalAcceleration": 3.68060473804244
}
```

## Axisymmetric J2 Gravity Field Components

Service ID: `axisymmetric-j2-gravity-field-components`. USD 1.00 per job.

Evaluate the exterior zonal degree-two gravitational potential and spherical components. No centrifugal acceleration, geopotential normalization conversion or full Earth field. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=axisymmetric-j2-gravity-field-components) · [Technical reference](https://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node73.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "mu": 1,
      "referenceRadius": 1,
      "j2": 0,
      "radius": 2,
      "geocentricLatitudeDegrees": 30
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/radialAcceleration": -0.25,
  "/records/0/latitudinalAcceleration": 0,
  "/records/0/potential": -0.5
}
```

## Glen Infinite Slab Glacier Flow Profile

Service ID: `glen-infinite-slab-glacier-flow-profile`. USD 1.00 per job.

Integrate Glen simple-shear deformation of an infinite uniform ice slab over a rigid bed with supplied basal sliding speed. No valley side drag, stress inversion or glacier hazard prediction. Thickness and sample height are normal to the inclined bed; speeds are downslope in the rotated parallel-slab coordinate system. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=glen-infinite-slab-glacier-flow-profile) · [Technical reference](https://ocw.hokudai.ac.jp/wp-content/uploads/2016/02/DynamicsOfIce-2005-Note-all.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "thickness": 1,
      "slopeDegrees": 30,
      "density": 1,
      "gravity": 2,
      "rateFactor": 1,
      "exponent": 3,
      "heightsAboveBed": [
        0,
        1
      ],
      "basalSpeed": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/speeds": [
    0,
    0.5
  ],
  "/records/0/meanSpeed": 0.4
}
```

## Snowpack Cold Content Melt Partition

Service ID: `snowpack-cold-content-melt-partition`. USD 1.00 per job.

Partition supplied nonnegative energy pulses into snow cold-content removal then latent melting with a finite snow mass. No refreezing, radiation calculation, avalanche or runoff forecast. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=snowpack-cold-content-melt-partition) · [Technical reference](https://raw.githubusercontent.com/peckhams/topoflow36/master/topoflow/components/snow_energy_balance.py)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "snowWaterEquivalentKgM2": 2,
      "initialTemperatureC": -1,
      "iceHeatCapacity": 1,
      "latentHeat": 2,
      "energyInputs": [
        1,
        3
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/coldContentRemaining": 0,
  "/records/0/meltKgM2": 1,
  "/records/0/remainingSnowKgM2": 1,
  "/records/0/unusedEnergy": 0
}
```

## Glacier Hypsometric Mass Balance Profile

Service ID: `glacier-hypsometric-mass-balance-profile`. USD 1.00 per job.

Integrate a supplied piecewise-linear capped glacier surface balance over fixed hypsometric bands. No evolving geometry, inferred equilibrium line or future glacier projection. The area ratio counts bands at or above the supplied equilibrium line; no equilibrium-line inversion is performed. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=glacier-hypsometric-mass-balance-profile) · [Technical reference](https://docs.oggm.org/en/stable/_modules/oggm/core/massbalance.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "bands": [
        {
          "area": 1,
          "elevation": 0
        },
        {
          "area": 1,
          "elevation": 2
        }
      ],
      "equilibriumLine": 1,
      "accumulationGradient": 1,
      "ablationGradient": 2,
      "accumulationCap": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/bandBalances": [
    -2,
    1
  ],
  "/records/0/meanBalance": -0.5,
  "/records/0/accumulationAreaRatio": 0.5
}
```

## Elastic Lithosphere Sinusoidal Load Flexure

Service ID: `elastic-lithosphere-sinusoidal-load-flexure`. USD 1.00 per job.

Solve static thin elastic plate flexure under one sinusoidal vertical load over a fluid foundation. Deflection follows load sign; no lithosphere inversion, fault failure or site design. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=elastic-lithosphere-sinusoidal-load-flexure) · [Technical reference](https://docs.generic-mapping-tools.org/latest/supplements/potential/grdflexure.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "youngModulus": 12,
      "elasticThickness": 1,
      "poissonRatio": 0,
      "densityContrast": 1,
      "gravity": 1,
      "wavenumber": 1,
      "loadAmplitude": 2,
      "positions": [
        0,
        3.141592653589793
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/rigidity": 1,
  "/records/0/deflections": [
    1,
    -1
  ],
  "/records/0/deflectionAmplitude": 1
}
```

## Cosmogenic Nuclide Exposure With Erosion

Service ID: `cosmogenic-nuclide-exposure-with-erosion`. USD 1.00 per job.

Evaluate a single-production-path surface cosmogenic-nuclide concentration under constant erosion, decay and inheritance. No shielding selection, actual exposure age or geological sample certification. Initial inherited concentration is uniform through the eroded material and decays only radioactively; erosion attenuation applies to the production history. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cosmogenic-nuclide-exposure-with-erosion) · [Technical reference](https://hess.ess.washington.edu/math/docs/al_be_stable/al_be_calc_paper_v2.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "productionRate": 2,
      "decayRate": 1,
      "density": 1,
      "erosionRate": 1,
      "attenuationMassLength": 1,
      "exposureTime": 0.6931471805599453,
      "inheritedConcentration": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/concentration": 0.75,
  "/records/0/effectiveLossRate": 2
}
```

## Uranium Lead Concordia Age Residual

Service ID: `uranium-lead-concordia-age-residual`. USD 1.00 per job.

Transform two supplied radiogenic daughter/parent ratios into closed-system U-Pb model ages and explicit discordance. Assumes no common lead, loss or inheritance correction; no dated geological-event claim. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=uranium-lead-concordia-age-residual) · [Technical reference](https://www.homepages.ucl.ac.uk/~ucfbpve/papers/VermeeschGSF2018/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "ratio206To238": 1,
      "ratio207To235": 3,
      "lambda238": 1,
      "lambda235": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/age206": 0.6931471805599453,
  "/records/0/age207": 0.6931471805599453,
  "/records/0/ageDifference": 0,
  "/records/0/discordanceFraction": 0
}
```

## Athy Exponential Sediment Decompaction

Service ID: `athy-exponential-sediment-decompaction`. USD 1.00 per job.

Restore a layer under Athy exponential porosity by conserving solid thickness between explicit burial positions. No lithology selection, diagenesis or stratigraphic-history inference. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=athy-exponential-sediment-decompaction) · [Technical reference](https://pybacktrack.readthedocs.io/_/downloads/en/latest/pdf/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "presentTop": 0,
      "presentBottom": 1,
      "surfacePorosity": 0,
      "compactionPerDepth": 1,
      "restoredTop": 2
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/solidThickness": 1,
  "/records/0/restoredBottom": 3,
  "/records/0/restoredThickness": 1
}
```

## Airy Sediment Load Backstripping Column

Service ID: `airy-sediment-load-backstripping-column`. USD 1.00 per job.

Backstrip a supplied compacted sediment column using local Airy compensation relative to water and mantle. No decompaction, sea-level/eustatic correction or inferred tectonic mechanism. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=airy-sediment-load-backstripping-column) · [Technical reference](https://pybacktrack.readthedocs.io/_/downloads/en/latest/pdf/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "waterDepth": 1,
      "waterDensity": 1,
      "mantleDensity": 3,
      "layers": [
        {
          "thickness": 2,
          "bulkDensity": 2
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/sedimentThickness": 2,
  "/records/0/tectonicSubsidence": 2,
  "/records/0/isostaticLoadSubsidence": 1
}
```

## Freezing Soil Enthalpy Transition Profile

Service ID: `freezing-soil-enthalpy-transition-profile`. USD 1.00 per job.

Evaluate a declared piecewise-linear unfrozen-water transition and corresponding soil enthalpy. Apparent heat capacity at transition endpoints uses the outside derivative convention; no empirical soil freezing curve. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=freezing-soil-enthalpy-transition-profile) · [Technical reference](https://doxygen.opengeosys.org/6.5.9/da/d01/ogs_file_param__properties__property__SpecificHeatCapacityWithLatentHeat.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "volumetricHeatCapacity": 2,
      "latentHeatPerVolume": 10,
      "transitionWidth": 1,
      "temperatures": [
        -1,
        -0.5,
        0,
        1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/liquidFractions": [
    0,
    0.5,
    1,
    1
  ],
  "/records/0/enthalpies": [
    -2,
    4,
    10,
    12
  ]
}
```

## Two Layer Seismic Refraction Travelcurve

Service ID: `two-layer-seismic-refraction-travelcurve`. USD 1.00 per job.

Build direct and critically refracted arrival times for a horizontal two-layer model with a faster half-space. Geometrically unavailable head waves are null; no picking or subsurface certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-layer-seismic-refraction-travelcurve) · [Technical reference](https://gpg.geosci.xyz/content/seismic/traveltimes.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "upperSpeed": 1,
      "lowerSpeed": 2,
      "interfaceDepth": 1,
      "offsets": [
        0,
        4
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/directTimes": [
    0,
    4
  ],
  "/records/0/criticalAngleDegrees": 30,
  "/records/0/interceptTime": 1.7320508075688772
}
```

## Dix Interval Velocity And Nmo

Service ID: `dix-interval-velocity-and-nmo`. USD 1.00 per job.

Derive Dix interval velocities and hyperbolic normal moveout times from supplied RMS velocities and two-way zero-offset times. Horizontal isotropic layers and small-offset approximation only. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dix-interval-velocity-and-nmo) · [Technical reference](https://sepwww.stanford.edu/data/media/public/docs/sep140/elita1/paper_html/node3.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "zeroOffsetTimes": [
        1,
        2
      ],
      "rmsVelocities": [
        2,
        3.1622776601683795
      ],
      "offset": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/intervalVelocities": [
    2,
    4
  ],
  "/records/0/moveoutTimes": [
    1,
    2
  ]
}
```

## Isotropic Elastic Wave Impedance State

Service ID: `isotropic-elastic-wave-impedance-state`. USD 1.00 per job.

Compute isotropic compressional/shear speeds, acoustic impedances and Poisson ratio from positive elastic moduli and density. No rock identification, anisotropy or material test validation. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=isotropic-elastic-wave-impedance-state) · [Technical reference](https://gpg.geosci.xyz/content/physical_properties/seismic_velocity_duplicate.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "bulkModulus": 2.6666666666666665,
      "shearModulus": 1,
      "density": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/pSpeed": 2,
  "/records/0/sSpeed": 1,
  "/records/0/pImpedance": 2,
  "/records/0/sImpedance": 1,
  "/records/0/poissonRatio": 0.3333333333333333
}
```

## Moment Tensor Far Field Radiation

Service ID: `moment-tensor-far-field-radiation`. USD 1.00 per job.

Resolve a symmetric seismic moment tensor into signed P and magnitude S far-field angular radiation factors. Omits distance, density, speed and time-function scale; no focal-mechanism inversion. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=moment-tensor-far-field-radiation) · [Technical reference](https://docs.obspy.org/_modules/obspy/core/event/source.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "tensor": [
        [
          1,
          0,
          0
        ],
        [
          0,
          -1,
          0
        ],
        [
          0,
          0,
          0
        ]
      ],
      "directions": [
        [
          1,
          0,
          0
        ],
        [
          0,
          0,
          1
        ]
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/pAmplitudes": [
    1,
    0
  ],
  "/records/0/sAmplitudes": [
    0,
    0
  ]
}
```

## Truncated Gutenberg Richter Count Bins

Service ID: `truncated-gutenberg-richter-count-bins`. USD 1.00 per job.

Allocate a supplied expected catalog total over finite magnitude bins under a normalized truncated Gutenberg-Richter model. No probability of damaging shaking, time forecast or fitted seismic hazard. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=truncated-gutenberg-richter-count-bins) · [Technical reference](https://earthquake.usgs.gov/data/oaf/background.php)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lowerMagnitude": 0,
      "upperMagnitude": 2,
      "bValue": 1,
      "totalExpected": 99,
      "edges": [
        0,
        1,
        2
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/expectedCounts": [
    90,
    9
  ]
}
```

## Modified Omori Interval Event Expectation

Service ID: `modified-omori-interval-event-expectation`. USD 1.00 per job.

Integrate a declared modified Omori aftershock rate over finite time intervals with a stable exponent-one limit. This is model arithmetic, not operational earthquake prediction or warning. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=modified-omori-interval-event-expectation) · [Technical reference](https://earthquake.usgs.gov/data/oaf/background.php)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "productivity": 1,
      "timeOffset": 1,
      "exponent": 1,
      "timeEdges": [
        0,
        1,
        3
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/expectedCounts": [
    0.6931471805599453,
    0.6931471805599453
  ]
}
```

## Vti Christoffel Phase Wave Speeds

Service ID: `vti-christoffel-phase-wave-speeds`. USD 1.00 per job.

Solve the VTI Christoffel matrix for the faster and slower coupled in-plane phase-speed roots and the separate SH phase speed. Positive elastic energy and eigenvalues are required. Root ordering is by speed; no P/S polarization classification or group/ray velocity is inferred. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=vti-christoffel-phase-wave-speeds) · [Technical reference](https://seismo.berkeley.edu/~wenk/TexturePage/Publications/2015-Geoph-Muderong.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "c11": 4,
      "c33": 4,
      "c44": 1,
      "c66": 1,
      "c13": 2,
      "density": 1,
      "anglesDegrees": [
        0,
        90
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/fastCoupledSpeeds": [
    2,
    2
  ],
  "/records/0/slowCoupledSpeeds": [
    1,
    1
  ],
  "/records/0/shSpeeds": [
    1,
    1
  ]
}
```

## Layered Seismic Ray Parameter Travel

Service ID: `layered-seismic-ray-parameter-travel`. USD 1.00 per job.

Trace a one-way transmitted ray through horizontal constant-speed layers at a supplied conserved horizontal slowness. Reflections, turning rays and source-location inversion are excluded. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=layered-seismic-ray-parameter-travel) · [Technical reference](https://gpg.geosci.xyz/content/seismic/traveltimes.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "layers": [
        {
          "thickness": 1,
          "speed": 2
        },
        {
          "thickness": 2,
          "speed": 4
        }
      ],
      "rayParameter": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/horizontalOffset": 0,
  "/records/0/travelTime": 1,
  "/records/0/anglesDegrees": [
    0,
    0
  ]
}
```

## Hypsometric Virtual Temperature Column

Service ID: `hypsometric-virtual-temperature-column`. USD 1.00 per job.

Integrate the hydrostatic hypsometric equation through piecewise constant layer-mean virtual temperature. Pressure units cancel; no sea-level reduction, sounding retrieval or altitude certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=hypsometric-virtual-temperature-column) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.thickness_hydrostatic.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pressures": [
        2,
        1
      ],
      "layerVirtualTemperatures": [
        300
      ],
      "gasConstant": 1,
      "gravity": 1,
      "baseHeight": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/heights": [
    10,
    217.94415416798358
  ],
  "/records/0/thickness": 207.94415416798358
}
```

## Dry Adiabatic Hydrostatic Parcel Column

Service ID: `dry-adiabatic-hydrostatic-parcel-column`. USD 1.00 per job.

Evaluate an unsaturated dry-adiabatic ideal-gas hydrostatic parcel column with fixed heat capacity and gravity. No moisture, entrainment or convective forecast. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dry-adiabatic-hydrostatic-parcel-column) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.dry_lapse.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "baseTemperature": 300,
      "basePressure": 1000,
      "gravity": 1,
      "heatCapacity": 1,
      "gasConstant": 1,
      "heights": [
        0,
        100
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/temperatures": [
    300,
    200
  ],
  "/records/0/pressures": [
    1000,
    666.6666666666666
  ]
}
```

## Signed Parcel Buoyancy Work Profile

Service ID: `signed-parcel-buoyancy-work-profile`. USD 1.00 per job.

Integrate positive and negative parcel buoyancy work with exact linear zero crossings. This does not identify LFC/EL or label full-profile work conventional CAPE/CIN; supplied virtual temperatures only. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=signed-parcel-buoyancy-work-profile) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.cape_cin.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "heights": [
        0,
        10,
        20
      ],
      "parcelVirtualTemperature": [
        300,
        303,
        300
      ],
      "environmentVirtualTemperature": [
        300,
        300,
        300
      ],
      "gravity": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/positiveWork": 1,
  "/records/0/negativeWork": 0,
  "/records/0/netWork": 1
}
```

## Layer Gradient Richardson Stability

Service ID: `layer-gradient-richardson-stability`. USD 1.00 per job.

Compute layer finite-difference gradient Richardson numbers and signed buoyancy frequency squared from potential temperature and vector wind. No turbulence threshold, mixing diagnosis or weather warning. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=layer-gradient-richardson-stability) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.gradient_richardson_number.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "heights": [
        0,
        10
      ],
      "potentialTemperatures": [
        300,
        303
      ],
      "eastWinds": [
        0,
        1
      ],
      "northWinds": [
        0,
        0
      ],
      "gravity": 10
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/richardsonNumbers": [
    0.9950248756218906
  ],
  "/records/0/buoyancyFrequenciesSquared": [
    0.009950248756218907
  ]
}
```

## Curved Isobar Gradient Wind Branch

Service ID: `curved-isobar-gradient-wind-branch`. USD 1.00 per job.

Solve signed-curvature gradient-wind balance for the branch continuous with geostrophic flow, in a positive-Coriolis frame. Anticyclonic limit is enforced; no observed wind or storm forecast. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=curved-isobar-gradient-wind-branch) · [Technical reference](https://www.eoas.ubc.ca/books/Practical_Meteorology/prmet102/Ch10-forces_winds-v102b.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "geostrophicSpeed": 2,
      "coriolis": 1,
      "curvatureRadius": 1,
      "cyclonic": true
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/gradientWind": 1,
  "/records/0/otherBranch": -2
}
```

## Shallow Water Potential Vorticity Stencil

Service ID: `shallow-water-potential-vorticity-stencil`. USD 1.00 per job.

Evaluate centered-stencil vertical vorticity and single-layer shallow-water potential vorticity at one cell. Inputs are collocated neighboring velocities; no spherical metric, boundary solver or atmospheric analysis. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=shallow-water-potential-vorticity-stencil) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.potential_vorticity_barotropic.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "eastWindNorth": 2,
      "eastWindSouth": 0,
      "northWindEast": 4,
      "northWindWest": 0,
      "cellSpacing": 1,
      "layerDepth": 2,
      "coriolis": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/relativeVorticity": 1,
  "/records/0/potentialVorticity": 1
}
```

## Stable Monin Obukhov Wind Profile

Service ID: `stable-monin-obukhov-wind-profile`. USD 1.00 per job.

Evaluate a stable log-linear Monin-Obukhov surface-layer wind profile with explicit displacement and neutral lower-bound reference. Only 0 <= z/L <= 1; no unstable branch or fitted stability. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=stable-monin-obukhov-wind-profile) · [Technical reference](https://www.eoas.ubc.ca/books/Practical_Meteorology/prmet102/Ch18-abl-v102.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "frictionVelocity": 0.4,
      "roughnessLength": 1,
      "obukhovLength": 100,
      "displacementHeight": 0,
      "heights": [
        2.718281828459045
      ],
      "vonKarman": 0.4,
      "stabilitySlope": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/windSpeeds": [
    1
  ]
}
```

## Constant Enthalpy Wet Bulb Root

Service ID: `constant-enthalpy-wet-bulb-root`. USD 1.00 per job.

Solve an explicitly approximate constant-moist-air-enthalpy saturation temperature using the stated Magnus vapour-pressure fit. Not a ventilated psychrometer, ASHRAE reference or heat-stress decision. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=constant-enthalpy-wet-bulb-root) · [Technical reference](https://psychrometrics.github.io/psychrolib/_modules/psychrolib.html#GetMoistAirEnthalpy)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "dryBulbCelsius": 20,
      "relativeHumidity": 1,
      "pressureKpa": 100
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/wetBulbCelsius": 20
}
```

## Bolton Lifting Condensation Parcel

Service ID: `bolton-lifting-condensation-parcel`. USD 1.00 per job.

Apply the Bolton approximate LCL temperature with a fixed dry-air Poisson exponent of 3.5 for pressure. Unsaturated parcel input only; no cloud-base observation or severe-weather forecast. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bolton-lifting-condensation-parcel) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.equivalent_potential_temperature.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "temperatureKelvin": 300,
      "dewpointKelvin": 300,
      "pressureHpa": 1000
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/lclTemperatureKelvin": 300,
  "/records/0/lclPressureHpa": 1000
}
```

## Fao56 Penman Monteith Reference Et

Service ID: `fao56-penman-monteith-reference-et`. USD 1.00 per job.

Evaluate the daily FAO-56 short-grass Penman-Monteith reference evapotranspiration equation from explicitly supplied meteorological terms. Negative values are preserved; no crop coefficient, irrigation scheduling or weather retrieval. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=fao56-penman-monteith-reference-et) · [Technical reference](https://www.fao.org/4/x0490e/x0490e06.htm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "netRadiationMJDay": 10,
      "soilHeatMJDay": 0,
      "meanTemperatureC": 27,
      "wind2m": 0,
      "saturationDeficitKpa": 0,
      "slopeKpaC": 0.1,
      "psychrometricKpaC": 0.1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/referenceEtMmDay": 2.04
}
```

## Trapezoidal Channel Critical Depth Root

Service ID: `trapezoidal-channel-critical-depth-root`. USD 1.00 per job.

Solve the minimum-specific-energy condition Q squared T = g A cubed for a trapezoidal open channel. Positive flow only; no backwater, bank stability or design certification. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=trapezoidal-channel-critical-depth-root) · [Technical reference](https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.5/theoretical-basis-for-one-dimensional-and-two-dimensional-hydrodynamic-calculations/1d-steady-flow-water-surface-profiles/critical-depth-determination)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "bottomWidth": 1,
      "sideSlope": 0,
      "discharge": 1,
      "gravity": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/criticalDepth": 1,
  "/records/0/specificEnergy": 1.5
}
```

## Part Full Circular Channel Critical Depth

Service ID: `part-full-circular-channel-critical-depth`. USD 1.00 per job.

Solve free-surface critical flow in a circular conduit using exact segment area and top width. Full pressurized pipe behavior, entrance loss and culvert approval are excluded. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=part-full-circular-channel-critical-depth) · [Technical reference](https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.5/theoretical-basis-for-one-dimensional-and-two-dimensional-hydrodynamic-calculations/1d-steady-flow-water-surface-profiles/critical-depth-determination)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "diameter": 2,
      "discharge": 1.392081999207927,
      "gravity": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/criticalDepth": 1,
  "/records/0/area": 1.5707963267948966,
  "/records/0/topWidth": 2
}
```

## Rectangular Standard Step Backwater

Service ID: `rectangular-standard-step-backwater`. USD 1.00 per job.

Solve one steady rectangular standard-step energy balance in a user-supplied root bracket with mean Manning friction slope. Root bracket selects regime; no hydraulic jump crossing, survey calibration or flood forecast. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rectangular-standard-step-backwater) · [Technical reference](https://www.txdot.gov/manuals/des/hyd/chapter-7--channels/section-6--channel-analysis-methods/standard-step-procedure.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "width": 1,
      "discharge": 1,
      "manning": 1,
      "gravity": 1,
      "length": 1,
      "bedDrop": 4.3267487109222245,
      "downstreamDepth": 1,
      "upstreamDepthBracket": [
        0.9,
        1.1
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/upstreamDepth": 1
}
```

## Compound Channel Divided Conveyance

Service ID: `compound-channel-divided-conveyance`. USD 1.00 per job.

Sum divided-section Manning conveyance at a common energy slope. Supplied section perimeters must omit artificial interfaces consistently; no automated subdivision or cross-section approval. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compound-channel-divided-conveyance) · [Technical reference](https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.5/theoretical-basis-for-one-dimensional-and-two-dimensional-hydrodynamic-calculations/1d-steady-flow-water-surface-profiles/cross-section-subdivision-for-conveyance-calculations)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "slope": 0.01,
      "sections": [
        {
          "area": 1,
          "wettedPerimeter": 1,
          "manning": 1
        },
        {
          "area": 2,
          "wettedPerimeter": 2,
          "manning": 2
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/conveyances": [
    1,
    1
  ],
  "/records/0/discharges": [
    0.1,
    0.1
  ],
  "/records/0/totalDischarge": 0.2
}
```

## Nonlinear Kinematic Wave Upwind Step

Service ID: `nonlinear-kinematic-wave-upwind-step`. USD 1.00 per job.

Advance a positive-downstream kinematic depth law q=coefficient times h to exponent using a conservative explicit upwind step. Courant and nonnegative-depth conditions reject; no dynamic-wave flood routing. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=nonlinear-kinematic-wave-upwind-step) · [Technical reference](https://mcirano.ufba.br/ftp/books/stewart05/book.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "depths": [
        1,
        1
      ],
      "inletDischarge": 1,
      "coefficient": 1,
      "exponent": 2,
      "cellLength": 1,
      "stepTime": 0.25,
      "rainRate": 0
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/depths": [
    1,
    1
  ],
  "/records/0/inletVolume": 0.25,
  "/records/0/outletVolume": 0.25,
  "/records/0/continuityResidual": 0
}
```

## Rouse Suspended Sediment Concentration Profile

Service ID: `rouse-suspended-sediment-concentration-profile`. USD 1.00 per job.

Evaluate the equilibrium Rouse concentration profile above a supplied reference height. Constant settling/friction velocities and diffusivity ratio one; no sediment calibration or ecological limit. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rouse-suspended-sediment-concentration-profile) · [Technical reference](https://ocw.mit.edu/courses/12-090-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/f12a550191dab303c925890aa6e474a3_ch10.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "depth": 2,
      "referenceHeight": 1,
      "referenceConcentration": 4,
      "settlingVelocity": 0.4,
      "frictionVelocity": 1,
      "vonKarman": 0.4,
      "sampleHeights": [
        1,
        1.5
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/rouseNumber": 1,
  "/records/0/concentrations": [
    4,
    1.3333333333333333
  ]
}
```

## Meyer Peter Muller Bedload Profile

Service ID: `meyer-peter-muller-bedload-profile`. USD 1.00 per job.

Evaluate the declared Meyer-Peter-Muller excess-Shields bedload law with explicit coefficient and threshold. No grain hiding, slope correction, parameter selection or channel-design approval. Shields values must represent grain-related shear or a plane bed. Outputs are solid sediment volume per unit width per time. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=meyer-peter-muller-bedload-profile) · [Technical reference](https://www.hec.usace.army.mil/confluence/rasdocs/d2sd/ras2dsedtr/6.0/model-description/transport-potential-formulas)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "shields": [
        0,
        0.5,
        1.5
      ],
      "criticalShields": 0.5,
      "relativeDensity": 2,
      "grainDiameter": 1,
      "gravity": 1,
      "coefficient": 8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/dimensionlessBedloads": [
    0,
    0,
    8
  ],
  "/records/0/volumeBedloads": [
    0,
    0,
    8
  ]
}
```

## Exner Bed Elevation Conservative Step

Service ID: `exner-bed-elevation-conservative-step`. USD 1.00 per job.

Apply one conservative Exner bed-elevation update from supplied face solid-sediment fluxes and constant porosity. Transport fluxes are supplied rather than inferred; no morphological forecast. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=exner-bed-elevation-conservative-step) · [Technical reference](https://www.hec.usace.army.mil/confluence/rasdocs/rassed1d/1d-sediment-transport-technical-reference-manual/sediment-continuity)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "bedElevations": [
        0,
        0
      ],
      "faceSedimentFlux": [
        0,
        1,
        0
      ],
      "porosity": 0.5,
      "cellLength": 1,
      "stepTime": 1
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/bedElevations": [
    -2,
    2
  ],
  "/records/0/solidVolumeChange": 0,
  "/records/0/boundarySolidVolume": 0
}
```

## Parallel Hazen Williams Branch Flow Split

Service ID: `parallel-hazen-williams-branch-flow-split`. USD 1.00 per job.

Resolve ideal parallel full-pipe branch flow using the SI Hazen-Williams empirical law with common head loss. No minor losses, viscosity correction, pressure safety or real network control. Supplied records and declared model only. No physical inspection, live access, control, professional certification or externally verified condition is provided. Supported model sizes and inputs are checked before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=parallel-hazen-williams-branch-flow-split) · [Technical reference](https://raw.githubusercontent.com/OpenWaterAnalytics/EPANET/dev/src/hydcoeffs.c)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "totalFlow": 2,
      "branches": [
        {
          "length": 1,
          "diameter": 1,
          "coefficient": 1
        },
        {
          "length": 1,
          "diameter": 1,
          "coefficient": 1
        }
      ]
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/branchFlows": [
    1,
    1
  ],
  "/records/0/headLoss": 10.67,
  "/records/0/flowResidual": 0
}
```

## Hargreaves Samani Daily Et Observation Report

Service ID: `hargreaves-samani-daily-et-observation-report`. USD 9.00 per job.

Reconcile a multi-day Hargreaves-Samani reference ET record in mm/day using extraterrestrial radiation expressed as equivalent evaporation mm/day. No FAO Penman-Monteith substitution, crop coefficient or irrigation advice. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=hargreaves-samani-daily-et-observation-report) · [Technical reference](https://pyeto.readthedocs.io/en/latest/_modules/pyeto/fao.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "days": [
        {
          "minimumC": 10,
          "maximumC": 14,
          "meanC": 12,
          "extraterrestrialRadiation": 10
        },
        {
          "minimumC": 10,
          "maximumC": 10,
          "meanC": 10,
          "extraterrestrialRadiation": 10
        }
      ],
      "observed": [
        1.3708,
        0
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1.3708,
    0
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Thornthwaite Annual Monthly Heat Index Report

Service ID: `thornthwaite-annual-monthly-heat-index-report`. USD 9.00 per job.

Reconcile all twelve monthly Thornthwaite potential-evapotranspiration values in mm using an annual heat index and explicit daylight/month-length adjustments. Positive-temperature branch only; no local validation or water-demand advice. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=thornthwaite-annual-monthly-heat-index-report) · [Technical reference](https://cran.r-project.org/web/packages/SPEI/SPEI.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "monthlyMeanC": [
        5,
        5,
        5,
        5,
        5,
        5,
        5,
        5,
        5,
        5,
        5,
        5
      ],
      "daylightHours": [
        12,
        12,
        12,
        12,
        12,
        12,
        12,
        12,
        12,
        12,
        12,
        12
      ],
      "daysInMonth": [
        30,
        30,
        30,
        30,
        30,
        30,
        30,
        30,
        30,
        30,
        30,
        30
      ],
      "observed": [
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084,
        43.29312375229084
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084,
    43.29312375229084
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Alternating Block Idf Storm Reconstruction Report

Service ID: `alternating-block-idf-storm-reconstruction-report`. USD 9.00 per job.

Reconstruct a finite alternating-block design hyetograph from one explicit IDF power law; output is depth per block and ties alternate right before left. Duration enters the IDF in minutes and intensity in mm/h. No return-period selection or storm forecast. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=alternating-block-idf-storm-reconstruction-report) · [Technical reference](https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/meteorology/precipitation/frequency-storm)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "blockMinutes": 60,
      "blocks": 2,
      "idfA": 7.745966692414834,
      "idfBMinutes": 0,
      "idfExponent": 0.5,
      "peakBlock": 0,
      "observed": [
        1,
        0.41421356237309515
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1,
    0.41421356237309515
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Glover Balmer Pumping History Water Balance Report

Service ID: `glover-balmer-pumping-history-water-balance-report`. USD 9.00 per job.

Reconcile an entire piecewise-constant nonnegative pumping history beside an ideal fully penetrating straight connected stream. Retain shutdown/post-shutdown depletion rates, cumulative stream-depletion volume, cumulative pumped volume and remaining aquifer-storage withdrawal at each supplied observation epoch. Finite pulses are integrated as positive contributions to avoid cancellation between distant step responses. Homogeneous constant-transmissivity aquifer and constant stream stage; no streambed resistance, site validation, ecological entitlement or pumping recommendation. Observed values are depletion rates in coherent volume/time units; volume diagnostics use the matching time unit. Active pulse response requires a²/elapsed<=400; larger unresolved response profiles reject. A positive asymptotic primitive at a²/elapsed>=50 avoids sharp-boundary quadrature failure; remaining kernels use relative convergence checks. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=glover-balmer-pumping-history-water-balance-report) · [Technical reference](https://raw.githubusercontent.com/FoundrySpatial/streamDepletr/master/R/glover.R)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "streamDistance": 2,
      "transmissivity": 1,
      "storativity": 1,
      "pumpingHistory": [
        {
          "time": 0,
          "rate": 1
        },
        {
          "time": 4,
          "rate": 0
        }
      ],
      "observationTimes": [
        1,
        4,
        9
      ],
      "observed": [
        0.1572992070502851,
        0.4795001221869534,
        0.11026263136839909
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.1572992070502851,
    0.4795001221869534,
    0.11026263136839909
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Radial Dupuit Circular Recharge Mound Report

Service ID: `radial-dupuit-circular-recharge-mound-report`. USD 9.00 per job.

Reconcile the unconfined Dupuit head mound from recharge over a circular pond and a concentric fixed-head outer boundary. Homogeneous horizontal base; no unsaturated travel, pond operation or real recharge prediction. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=radial-dupuit-circular-recharge-mound-report) · [Technical reference](https://portal.ct.gov/-/media/deep/water_regulating_and_discharges/subsurface/2006designmanual/completesec6pdf.pdf?hash=28942C042A4FCD37D0C9FD287BADFEEE&rev=16f42925ef994d8e8b670c74b15a4f6b)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "conductivity": 1,
      "pondRadius": 1,
      "boundaryRadius": 2,
      "boundaryHead": 1,
      "recharge": 1,
      "radii": [
        1,
        2
      ],
      "observed": [
        1.3012098910475378,
        1
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1.3012098910475378,
    1
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Water Table Fluctuation Recession Recharge Report

Service ID: `water-table-fluctuation-recession-recharge-report`. USD 9.00 per job.

Reconcile positive recharge pulses by the water-table-fluctuation method after a supplied constant recession correction. Negative residual rises contribute zero recharge but signed observed storage change is retained. No specific-yield estimation or groundwater forecast. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=water-table-fluctuation-recession-recharge-report) · [Technical reference](https://www.usgs.gov/mission-areas/water-resources/science/water-table-fluctuation-method)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "specificYield": 0.2,
      "times": [
        0,
        1,
        2
      ],
      "waterLevels": [
        0,
        1,
        0.5
      ],
      "recessionRate": 0.5,
      "observed": [
        0.3,
        0
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.3,
    0
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Eckhardt Recession Hydrograph Partition Report

Service ID: `eckhardt-recession-hydrograph-partition-report`. USD 9.00 per job.

Reconcile a complete Eckhardt baseflow/direct-flow partition after pooled within-segment exponential recession fitting from supplied strictly declining dry periods. Uniform-interval streamflow values are interval means; supplied initial baseflow and BFImax are explicit assumptions. Published baseflow<=streamflow constraint is retained with constrained-step count and separate conserved water volumes. No calibration against actual groundwater discharge, event classification or flow recommendation. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=eckhardt-recession-hydrograph-partition-report) · [Technical reference](https://hess.copernicus.org/articles/27/495/2023/hess-27-495-2023.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "recessionSegments": [
        [
          8,
          4,
          2
        ],
        [
          4,
          2,
          1
        ]
      ],
      "streamflows": [
        4,
        12,
        6,
        1,
        0
      ],
      "initialBaseflow": 2,
      "maximumBaseflowIndex": 0.5,
      "intervalDuration": 2,
      "observed": [
        2,
        4.666666666666667,
        3.5555555555555554,
        1,
        0
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    2,
    4.666666666666667,
    3.5555555555555554,
    1,
    0
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Brooks Corey Drainage Hydraulic Series Report

Service ID: `brooks-corey-drainage-hydraulic-series-report`. USD 9.00 per job.

Reconcile a complete Brooks-Corey drainage retention series with its specified Burdine conductivity exponent 3+2/lambda. Air-entry plateau is explicit; no fitted pore-size distribution or soil suitability advice. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=brooks-corey-drainage-hydraulic-series-report) · [Technical reference](https://wwwbrr.cr.usgs.gov/projects/GW_Unsat/vs2di/hlp/solute/brooksCorey.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "airEntryHead": 1,
      "poreIndex": 1,
      "residualWater": 0,
      "saturatedWater": 1,
      "saturatedConductivity": 1,
      "suctions": [
        1,
        2
      ],
      "observed": [
        1,
        0.5
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1,
    0.5
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Kosugi Lognormal Soil Retention Series Report

Service ID: `kosugi-lognormal-soil-retention-series-report`. USD 9.00 per job.

Reconcile an explicitly lognormal Kosugi equilibrium soil-retention curve over supplied suction magnitudes. Zero suction has exact saturation; no fitted distribution, hysteresis or irrigation action. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=kosugi-lognormal-soil-retention-series-report) · [Technical reference](https://hess.copernicus.org/articles/27/1565/2023/hess-27-1565-2023.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "medianHead": 1,
      "logSigma": 1,
      "residualWater": 0,
      "saturatedWater": 1,
      "suctions": [
        0,
        1
      ],
      "observed": [
        1,
        0.5
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1,
    0.5
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Bolton Equivalent Potential Temperature Sounding Report

Service ID: `bolton-equivalent-potential-temperature-sounding-report`. USD 9.00 per job.

Reconcile a full Bolton-1980 equivalent-potential-temperature sounding in K from pressure, temperature and dewpoint. The LCL expression is one intermediate term; no parcel trajectory, CAPE or weather warning. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bolton-equivalent-potential-temperature-sounding-report) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.equivalent_potential_temperature.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "levels": [
        {
          "temperatureK": 300,
          "dewpointK": 300,
          "pressureHpa": 1000
        },
        {
          "temperatureK": 300,
          "dewpointK": 300,
          "pressureHpa": 1000
        }
      ],
      "observed": [
        367.25692222448777,
        367.25692222448777
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    367.25692222448777,
    367.25692222448777
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Murphy Koop Ice Saturation Observation Report

Service ID: `murphy-koop-ice-saturation-observation-report`. USD 9.00 per job.

Reconcile equilibrium vapour pressure in Pa over a plane ice surface using Murphy-Koop 2005 equation7 across a supplied temperature series. No pressure enhancement factor, supercooled-water substitution or atmospheric validation. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=murphy-koop-ice-saturation-observation-report) · [Technical reference](https://github.com/NCAR/Ranadu/blob/master/R/MurphyKoop.R)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "temperaturesK": [
        250,
        273.16
      ],
      "observed": [
        76.0238900365987,
        611.6570688068414
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    76.0238900365987,
    611.6570688068414
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Garcia Gordon Seawater Oxygen Saturation Report

Service ID: `garcia-gordon-seawater-oxygen-saturation-report`. USD 9.00 per job.

Reconcile air-equilibrium dissolved oxygen in umol/kg at 101325 Pa using Garcia-Gordon coefficients and the GSW ITS-90-to-IPTS-68 conversion. No pressure correction or water-quality pass; this auxiliary algorithm is not IOC approved. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=garcia-gordon-seawater-oxygen-saturation-report) · [Technical reference](https://www.teos-10.org/pubs/gsw/html/gsw_O2sol_SP_pt.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "samples": [
        {
          "salinity": 34.7118,
          "potentialTemperatureC": 28.8099
        },
        {
          "salinity": 34.8915,
          "potentialTemperatureC": 28.4392
        }
      ],
      "observed": [
        194.682543169294,
        195.6135062814438
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    194.682543169294,
    195.6135062814438
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Mackenzie Seawater Sound Speed Cast Report

Service ID: `mackenzie-seawater-sound-speed-cast-report`. USD 9.00 per job.

Reconcile a hydrographic sound-speed cast in m/s with the Mackenzie nine-term empirical equation over its declared T,S,depth profile. No acoustic-path bending, depth conversion or sonar control. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mackenzie-seawater-sound-speed-cast-report) · [Technical reference](https://resource.npl.co.uk/acoustics/techguides/soundseawater/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "samples": [
        {
          "temperatureC": 10,
          "salinity": 35,
          "depthMetres": 0
        },
        {
          "temperatureC": 20,
          "salinity": 35,
          "depthMetres": 0
        }
      ],
      "observed": [
        1489.8034,
        1521.4632
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1489.8034,
    1521.4632
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Unesco Seawater Freezing Cast Report

Service ID: `unesco-seawater-freezing-cast-report`. USD 9.00 per job.

Reconcile the UNESCO-1983 practical-salinity freezing curve in ITS-90 degrees C, including the IPTS-68-to-ITS-90 conversion and sea-pressure term. No TEOS-10 brine equilibrium, ice nucleation or physical freezing claim. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=unesco-seawater-freezing-cast-report) · [Technical reference](https://pythonhosted.org/seawater/eos80.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "samples": [
        {
          "salinity": 0,
          "pressureDbar": 0
        },
        {
          "salinity": 0,
          "pressureDbar": 1000
        }
      ],
      "observed": [
        0,
        -0.752819323362393
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0,
    -0.752819323362393
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Finite Bottom Ekman Current Observation Report

Service ID: `finite-bottom-ekman-current-observation-report`. USD 9.00 per job.

Reconcile current-speed observations with a constant-viscosity Ekman layer subject to supplied surface stress and a no-slip finite seabed. Signed Coriolis and depths positive down; no current forecast or bottom-stress calibration. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-bottom-ekman-current-observation-report) · [Technical reference](https://www.jmlilly.net/doc/windtrans.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "windStressEast": 1,
      "windStressNorth": 0,
      "density": 1,
      "eddyViscosity": 1,
      "coriolis": 0.02,
      "waterDepth": 31.41592653589793,
      "depths": [
        0,
        31.41592653589793
      ],
      "observed": [
        7.044707410024933,
        0
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    7.044707410024933,
    0
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Finite Depth Stokes Drift Column Report

Service ID: `finite-depth-stokes-drift-column-report`. USD 9.00 per job.

Reconcile second-order Lagrangian Stokes drift versus positive-down depth for one small-amplitude finite-depth gravity wave. No return current, breaking or surface drift forecast. Amplitude/depth is bounded at0.1 as well as wave steepness; these are supplied-model profile bounds, not actual sea-state validation. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-depth-stokes-drift-column-report) · [Technical reference](https://www.pure.ed.ac.uk/ws/portalfiles/portal/45221950/VandenBremer_Breivik_R1_submitted.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "amplitude": 0.1,
      "period": 7.1997607828454475,
      "depth": 1,
      "gravity": 1,
      "sampleDepths": [
        0,
        1
      ],
      "observed": [
        0.01188635617228823,
        0.0031594199633099315
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.01188635617228823,
    0.0031594199633099315
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Smb Fetch Limited Wave Growth Report

Service ID: `smb-fetch-limited-wave-growth-report`. USD 9.00 per job.

Reconcile fetch-limited deep-water SMB significant wave height and significant period Ts from an explicitly supplied adjusted wind parameter. Adequate wind duration and deep water are assumptions; no raw-to-adjusted wind conversion, peak-period estimate, duration-limit check or actual wave forecast. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=smb-fetch-limited-wave-growth-report) · [Technical reference](https://www.civil.iitb.ac.in/~mcdeo/waves_book1/wave.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "adjustedWindSpeed": 1,
      "gravity": 1,
      "fetches": [
        0,
        1
      ],
      "observed": [
        0,
        0.0035373157667229044
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0,
    0.0035373157667229044
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Two Layer Kdv Internal Soliton Report

Service ID: `two-layer-kdv-internal-soliton-report`. USD 9.00 per job.

Reconcile a weakly nonlinear two-layer KdV internal solitary-wave interface profile, width and celerity. Interface sign follows alpha times amplitude positive; no breaking, shear or internal-wave forecast. Boussinesq rigid-lid interface displacement is positive upward; layer-depth difference must be at least 10 percent of the shallower depth to exclude near-critical quadratic nonlinearity. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=two-layer-kdv-internal-soliton-report) · [Technical reference](https://iris.uniroma1.it/retrieve/e3835327-bea7-15e8-e053-a505fe0a3de9/Tesi_dottorato_Cavaliere.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "upperDepth": 2,
      "lowerDepth": 1,
      "reducedGravity": 1,
      "amplitude": 0.1,
      "positions": [
        0,
        6.436642602664616
      ],
      "observed": [
        0.1,
        0.05
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.1,
    0.05
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Petterssen Frontogenesis Gradient Observation Report

Service ID: `petterssen-frontogenesis-gradient-observation-report`. USD 9.00 per job.

Reconcile Cartesian two-dimensional Petterssen kinematic frontogenesis from supplied potential-temperature and wind gradients. The signed material change of thermal-gradient magnitude is retained; no front identification or weather forecast. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=petterssen-frontogenesis-gradient-observation-report) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.frontogenesis.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cells": [
        {
          "thetaEastGradient": 1,
          "thetaNorthGradient": 0,
          "duDx": -1,
          "duDy": 0,
          "dvDx": 0,
          "dvDy": 1
        },
        {
          "thetaEastGradient": 1,
          "thetaNorthGradient": 0,
          "duDx": 1,
          "duDy": 0,
          "dvDx": 0,
          "dvDy": -1
        }
      ],
      "observed": [
        1,
        -1
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1,
    -1
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Quasigeostrophic Q Vector Forcing Report

Service ID: `quasigeostrophic-q-vector-forcing-report`. USD 9.00 per job.

Reconcile Q-vector magnitudes and components from supplied geostrophic wind/temperature gradients under a declared pressure-coordinate static-stability scaling. No Q divergence, omega inversion or weather forecast. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=quasigeostrophic-q-vector-forcing-report) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.q_vector.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gasConstant": 1,
      "pressure": 1,
      "staticStability": 1,
      "cells": [
        {
          "temperatureEastGradient": 1,
          "temperatureNorthGradient": 2,
          "duDx": 1,
          "duDy": 0,
          "dvDx": 0,
          "dvDy": 1
        },
        {
          "temperatureEastGradient": 1,
          "temperatureNorthGradient": 0,
          "duDx": 0,
          "duDy": 1,
          "dvDx": 0,
          "dvDy": 0
        }
      ],
      "observed": [
        2.23606797749979,
        1
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    2.23606797749979,
    1
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Ertel Baroclinic Potential Vorticity Report

Service ID: `ertel-baroclinic-potential-vorticity-report`. USD 9.00 per job.

Reconcile pressure-coordinate Ertel baroclinic potential vorticity including horizontal thermal gradients and vertical wind shear. All derivatives must share pressure and Cartesian conventions; no PV anomaly or weather interpretation. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ertel-baroclinic-potential-vorticity-report) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.potential_vorticity_baroclinic.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "gravity": 1,
      "cells": [
        {
          "duDp": 0,
          "dvDp": 0,
          "dThetaDx": 0,
          "dThetaDy": 0,
          "dThetaDp": -2,
          "relativeVorticity": 1,
          "coriolis": 1
        },
        {
          "duDp": 1,
          "dvDp": 0,
          "dThetaDx": 0,
          "dThetaDy": 2,
          "dThetaDp": -2,
          "relativeVorticity": 1,
          "coriolis": 1
        }
      ],
      "observed": [
        4,
        2
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    4,
    2
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Bunkers Hodograph Helicity Observation Report

Service ID: `bunkers-hodograph-helicity-observation-report`. USD 9.00 per job.

Reconcile right/left Bunkers non-pressure-weighted motion and 0 to 6 km storm-relative helicities from one supplied hodograph and explicit deviation speed. No actual storm track, severe-weather probability or warning. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bunkers-hodograph-helicity-observation-report) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.bunkers_storm_motion.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "heightsMetres": [
        0,
        3000,
        6000
      ],
      "eastWinds": [
        0,
        5,
        10
      ],
      "northWinds": [
        0,
        0,
        0
      ],
      "deviationSpeed": 7.5,
      "observed": [
        75,
        -75
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    75,
    -75
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Isentropic Pressure Temperature Reconstruction Report

Service ID: `isentropic-pressure-temperature-reconstruction-report`. USD 9.00 per job.

Reconstruct pressures and temperatures of supplied isentropes from a decreasing-pressure sounding with temperature linear in log pressure inside each layer. Potential temperature must rise monotonically; no extrapolation or weather-data retrieval. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=isentropic-pressure-temperature-reconstruction-report) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.isentropic_interpolation.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "pressureHpa": [
        1000,
        250
      ],
      "temperatureK": [
        300,
        300
      ],
      "thetaTargets": [
        300,
        600
      ],
      "kappa": 0.5,
      "observed": [
        1000,
        250
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1000,
    250
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Pseudoadiabatic Moist Parcel Observation Report

Service ID: `pseudoadiabatic-moist-parcel-observation-report`. USD 9.00 per job.

Reconcile a saturated pseudoadiabatic parcel temperature path by RK4 in log pressure using explicit thermodynamic constants and a liquid-water saturation fit. Fixed latent heat and instantaneous condensate removal; no mixed-phase, entrainment, CAPE or forecast. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pseudoadiabatic-moist-parcel-observation-report) · [Technical reference](https://unidata.github.io/MetPy/latest/api/generated/metpy.calc.moist_lapse.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "basePressurePa": 100000,
      "baseTemperatureK": 300,
      "targetPressurePa": [
        100000,
        25000
      ],
      "gasConstantDry": 1,
      "heatCapacityDry": 2,
      "epsilon": 0.622,
      "latentHeat": 0,
      "observed": [
        300,
        150
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    300,
    150
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Kappa Kohler Cloud Droplet Activation Report

Service ID: `kappa-kohler-cloud-droplet-activation-report`. USD 9.00 per job.

Reconcile exact kappa-Kohler critical supersaturations and wet radii for dry aerosol sizes using a declared Kelvin length. Same length units and ideal solution parameterization; no aerosol composition inference or actual cloud activation claim. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=kappa-kohler-cloud-droplet-activation-report) · [Technical reference](https://acp.copernicus.org/articles/7/1961/2007/acp-7-1961-2007.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "dryRadii": [
        1,
        2
      ],
      "kappa": 1,
      "kelvinLength": 1,
      "observed": [
        0.4460153316800488,
        0.14326640604148855
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.4460153316800488,
    0.14326640604148855
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Spherical Exponential Atmosphere Optical Column Report

Service ID: `spherical-exponential-atmosphere-optical-column-report`. USD 9.00 per job.

Reconcile slant optical depth by integrating number density along straight rays through a spherical exponential atmosphere to 40 scale heights. No refraction or scattering source term; vertical rays use the exact infinite-column limit. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=spherical-exponential-atmosphere-optical-column-report) · [Technical reference](https://acp.copernicus.org/articles/24/5093/2024/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "earthRadius": 1000,
      "scaleHeight": 1,
      "surfaceNumberDensity": 1,
      "crossSection": 1,
      "zenithDegrees": [
        0,
        0
      ],
      "observed": [
        1,
        1
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1,
    1
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Point Mass Weak Light Deflection Observation Report

Service ID: `point-mass-weak-light-deflection-observation-report`. USD 9.00 per job.

Reconcile first-order general-relativistic angular light deflection by a point mass for distant source directions. Body vector points from observer toward mass; small tangent deflections are normalized geometrically. No close-limb occultation, multiple masses or astrometric catalog qualification. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=point-mass-weak-light-deflection-observation-report) · [Technical reference](https://www.iausofa.org/2023-10-11c#documentation)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "muOverC2": 0.001,
      "observerBodyDirection": [
        1,
        0,
        0
      ],
      "observerBodyDistance": 1,
      "sourceDirections": [
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "observed": [
        0.0019999973333397333,
        0.0019999973333397333
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.0019999973333397333,
    0.0019999973333397333
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Moving Target Retarded Range Observation Report

Service ID: `moving-target-retarded-range-observation-report`. USD 9.00 per job.

Reconcile finite-light-speed retarded ranges to a target moving at constant subluminal velocity relative to a fixed receiver. States refer to reception time; no ephemeris lookup, acceleration or relativistic aberration. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=moving-target-retarded-range-observation-report) · [Technical reference](https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/abcorr.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "targetVelocity": [
        0.5,
        0,
        0
      ],
      "relativePositionsAtReception": [
        [
          1,
          0,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "lightSpeed": 1,
      "observed": [
        0.6666666666666666,
        1.3333333333333333
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.6666666666666666,
    1.3333333333333333
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Shapiro Point Mass Path Delay Observation Report

Service ID: `shapiro-point-mass-path-delay-observation-report`. USD 9.00 per job.

Reconcile the first-post-Newtonian point-mass Shapiro excess propagation time along nondegenerate endpoint geometry. No occultation screening, multiple-body corrections or actual tracking-system timing qualification. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=shapiro-point-mass-path-delay-observation-report) · [Technical reference](https://github.com/tudat-team/tudatpy/blob/develop/src/tudat/astro/relativity/relativisticLightTimeCorrection.cpp)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "mu": 0.001,
      "lightSpeed": 1,
      "paths": [
        {
          "observerRadius": 2,
          "targetRadius": 2,
          "separation": 2
        },
        {
          "observerRadius": 3,
          "targetRadius": 3,
          "separation": 3
        }
      ],
      "observed": [
        0.0021972245773362194,
        0.0021972245773362194
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.0021972245773362194,
    0.0021972245773362194
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Henyey Greenstein Angular Scattering Report

Service ID: `henyey-greenstein-angular-scattering-report`. USD 9.00 per job.

Reconcile exact solid-angle bin fractions under the normalized Henyey-Greenstein single-scattering phase function. Edges are polar angles about incident direction; no multiple scattering, polarization or atmosphere fit. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=henyey-greenstein-angular-scattering-report) · [Technical reference](https://pbr-book.org/4ed/Volume_Scattering/Phase_Functions)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "asymmetry": 0,
      "angleEdgesDegrees": [
        0,
        90,
        180
      ],
      "observed": [
        0.5,
        0.5
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.5,
    0.5
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Lead210 Crs Sediment Age Depth Report

Service ID: `lead210-crs-sediment-age-depth-report`. USD 9.00 per job.

Reconcile top-of-layer Pb-210 constant-rate-of-supply model ages from dry mass and unsupported activities. Core is assumed to capture the full inventory; the infinite-age bottom boundary is excluded. No actual sediment chronology certification. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lead210-crs-sediment-age-depth-report) · [Technical reference](https://paleolimbot.github.io/pb210/reference/pb210_cic.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "decayRatePerYear": 1,
      "layers": [
        {
          "dryMassPerArea": 1,
          "totalActivity": 2,
          "supportedActivity": 1
        },
        {
          "dryMassPerArea": 1,
          "totalActivity": 2,
          "supportedActivity": 1
        }
      ],
      "observed": [
        0,
        0.6931471805599453
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0,
    0.6931471805599453
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Radiocarbon Calibration Grid Posterior Report

Service ID: `radiocarbon-calibration-grid-posterior-report`. USD 9.00 per job.

Reconcile a finite radiocarbon calibration posterior over supplied discrete calendar-age prior masses and a possibly nonmonotone calibration curve with Gaussian uncertainty. Highest-posterior grid sets may be disconnected; no calibration curve retrieval, reservoir correction or archaeological date certification. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=radiocarbon-calibration-grid-posterior-report) · [Technical reference](https://c14.arch.ox.ac.uk/oxcalhelp/hlp_analysis_detail.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "measuredAge": 0,
      "measurementSigma": 1,
      "credibleMass": 0.68,
      "grid": [
        {
          "calendarAge": 0,
          "curveAge": 0,
          "curveSigma": 0,
          "priorMass": 1
        },
        {
          "calendarAge": 1,
          "curveAge": 1,
          "curveSigma": 0,
          "priorMass": 1
        },
        {
          "calendarAge": 2,
          "curveAge": 0,
          "curveSigma": 0,
          "priorMass": 1
        }
      ],
      "observed": [
        0.38365173119055074,
        0.23269653761889864,
        0.38365173119055074
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.38365173119055074,
    0.23269653761889864,
    0.38365173119055074
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Rubidium Strontium Isochron Observation Report

Service ID: `rubidium-strontium-isochron-observation-report`. USD 9.00 per job.

Reconcile closed-system Rb-Sr isochron model ages and initial daughter ratios from multiple cogenetic sample sets by unweighted ordinary least squares. No errors-in-variables regression, common-source proof or geological event certification. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rubidium-strontium-isochron-observation-report) · [Technical reference](https://www.homepages.ucl.ac.uk/~ucfbpve/papers/VermeeschGSF2018/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "decayRate": 1,
      "isochrons": [
        [
          {
            "parentRatio": 1,
            "daughterRatio": 2
          },
          {
            "parentRatio": 2,
            "daughterRatio": 3
          },
          {
            "parentRatio": 3,
            "daughterRatio": 4
          }
        ],
        [
          {
            "parentRatio": 1,
            "daughterRatio": 4
          },
          {
            "parentRatio": 2,
            "daughterRatio": 7
          },
          {
            "parentRatio": 3,
            "daughterRatio": 10
          }
        ]
      ],
      "observed": [
        0.6931471805599453,
        1.3862943611198906
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.6931471805599453,
    1.3862943611198906
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Uranium Thorium Disequilibrium Age Report

Service ID: `uranium-thorium-disequilibrium-age-report`. USD 9.00 per job.

Reconcile closed-system U-Th disequilibrium model ages from present activity ratios with initial 234U excess and no initial 230Th. Decay constants and maximum bracket share time units; near-saturation profiles reject. No detrital correction or dated-event claim. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=uranium-thorium-disequilibrium-age-report) · [Technical reference](https://www.homepages.ucl.ac.uk/~ucfbpve/papers/VermeeschGSF2018/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "lambda230": 2,
      "lambda234": 1,
      "maximumAge": 10,
      "samples": [
        {
          "activity234To238": 1.5,
          "activity230To238": 1.25
        },
        {
          "activity234To238": 1,
          "activity230To238": 0.75
        }
      ],
      "observed": [
        0.6931471805599453,
        0.6931471805599453
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.6931471805599453,
    0.6931471805599453
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Layered Radiogenic Geotherm Observation Report

Service ID: `layered-radiogenic-geotherm-observation-report`. USD 9.00 per job.

Reconcile a steady layered conductive geotherm with uniform volumetric radiogenic heat production in each layer and continuous temperature/heat flux. Depth is positive down and heat flux positive up; no groundwater advection, fitted geology or geothermal resource certification. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=layered-radiogenic-geotherm-observation-report) · [Technical reference](https://aspect-documentation.readthedocs.io/en/v3.0.0/user/cookbooks/cookbooks/continental_extension/doc/continental_extension.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "surfaceTemperature": 0,
      "surfaceUpwardHeatFlux": 3,
      "layers": [
        {
          "thickness": 1,
          "conductivity": 1,
          "heatProduction": 1
        },
        {
          "thickness": 1,
          "conductivity": 1,
          "heatProduction": 1
        }
      ],
      "observed": [
        2.5,
        4
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    2.5,
    4
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Rusle Hillslope Soil Loss Observation Report

Service ID: `rusle-hillslope-soil-loss-observation-report`. USD 9.00 per job.

Reconcile RUSLE-style hillslope soil-loss records using explicit R,K,C,P inputs and McCool slope-length/steepness factors. R and K must share a compatible soil-loss unit system. No calibrated erosion forecast, conservation-plan approval or site suitability. Length is the horizontal slope projection and must be at least 4.572 m (15 ft); moderate rill/interrill susceptibility is assumed. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=rusle-hillslope-soil-loss-observation-report) · [Technical reference](https://www.ars.usda.gov/ARSUserFiles/60600505/RUSLE/AH_703%20-%20Predicting%20Soil%20Erosion%20by%20Water%20-%20A%20Guide%20to%20Conservation%20Planning%20With%20the%20RUSLE%20%28RUSLE%29.pdf)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "erosivity": 1,
      "erodibility": 1,
      "segments": [
        {
          "slopeLengthMetres": 22.13,
          "slopeDegrees": 0,
          "coverFactor": 1,
          "supportFactor": 1
        },
        {
          "slopeLengthMetres": 22.13,
          "slopeDegrees": 5.739170477266787,
          "coverFactor": 1,
          "supportFactor": 1
        }
      ],
      "observed": [
        0.03,
        1.18
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    0.03,
    1.18
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Infinite Slope Effective Stress Observation Report

Service ID: `infinite-slope-effective-stress-observation-report`. USD 9.00 per job.

Reconcile the explicit infinite-slope effective-stress force-balance ratio over supplied homogeneous cases. Vertical soil depth convention is fixed; no finite slip surface, site safety threshold, groundwater prediction or engineering approval. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=infinite-slope-effective-stress-observation-report) · [Technical reference](https://landlab.readthedocs.io/en/v2.9.1/_modules/landlab/components/landslides/landslide_probability.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "cases": [
        {
          "unitWeight": 1,
          "verticalDepth": 1,
          "slopeDegrees": 30,
          "cohesion": 1,
          "frictionDegrees": 0,
          "porePressure": 0
        },
        {
          "unitWeight": 1,
          "verticalDepth": 1,
          "slopeDegrees": 30,
          "cohesion": 2,
          "frictionDegrees": 0,
          "porePressure": 0
        }
      ],
      "observed": [
        2.3094010767585034,
        4.618802153517007
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    2.3094010767585034,
    4.618802153517007
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Bishop Simplified Slice Equilibrium Report

Service ID: `bishop-simplified-slice-equilibrium-report`. USD 9.00 per job.

Reconcile simplified Bishop circular-slip slice moment ratios for supplied positive-base-angle profiles by solving the implicit friction equation. Slip geometry and pore pressures are supplied; no minimum-surface search, interslice-force accuracy or slope safety approval. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bishop-simplified-slice-equilibrium-report) · [Technical reference](https://xslope.org/en/latest/lem/bishop/)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "slips": [
        [
          {
            "weight": 1,
            "width": 1,
            "baseDegrees": 30,
            "cohesion": 1,
            "frictionDegrees": 0,
            "porePressure": 0
          }
        ],
        [
          {
            "weight": 1,
            "width": 1,
            "baseDegrees": 30,
            "cohesion": 0,
            "frictionDegrees": 30,
            "porePressure": 0
          }
        ]
      ],
      "observed": [
        2.3094010767585034,
        1
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    2.3094010767585034,
    1
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Hoek Brown Rock Mass Envelope Report

Service ID: `hoek-brown-rock-mass-envelope-report`. USD 9.00 per job.

Reconcile the generalized Hoek-Brown compressive rock-mass failure envelope from explicit GSI, disturbance, intact strength and mi. Compressive confinement only; no field index validation, tensile branch or excavation design approval. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=hoek-brown-rock-mass-envelope-report) · [Technical reference](https://www.rocscience.com/help/rsdata/documentation/materials/strength-criterion/generalized-hoek-brown-criterion)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "intactStrength": 1,
      "mi": 1,
      "gsi": 100,
      "disturbance": 0,
      "confiningStresses": [
        0,
        3
      ],
      "observed": [
        1,
        5
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1,
    5
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## Heterogeneous Steady Darcy Grid Observation Report

Service ID: `heterogeneous-steady-darcy-grid-observation-report`. USD 9.00 per job.

Reconcile monitor-cell heads from a steady Cartesian heterogeneous Darcy finite-volume grid with harmonic face conductance and fixed perimeter. Source uses the units required by div(K grad h)+source=0; bounded Gauss-Seidel convergence is required. No calibrated groundwater forecast or pumping operation. Both relative iterate change and normalized discrete flux-balance residual must be at most 1e-12 without a unit-size absolute floor. Source underflow rejects. Predictions, signed residuals, RMS, maximum residual and the number beyond the supplied absolute tolerance are retained. A finding marks a supplied observation discrepancy; it is not a physical or professional pass. Deterministic supplied-data model only. Supported model sizes and inputs are checked before checkout. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=heterogeneous-steady-darcy-grid-observation-report) · [Technical reference](https://modflow6.readthedocs.io/en/latest/_mf6io/gwf-npf.html)

Example input:

```json
{
  "records": [
    {
      "id": "R1",
      "grid": [
        [
          {
            "head": 0,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          },
          {
            "head": 1,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          },
          {
            "head": 2,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          }
        ],
        [
          {
            "head": 0,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          },
          {
            "head": 0,
            "conductivity": 1,
            "fixed": false,
            "source": 0
          },
          {
            "head": 2,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          }
        ],
        [
          {
            "head": 0,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          },
          {
            "head": 1,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          },
          {
            "head": 2,
            "conductivity": 1,
            "fixed": true,
            "source": 0
          }
        ]
      ],
      "cellSpacing": 1,
      "observationCells": [
        [
          1,
          1
        ],
        [
          0,
          2
        ]
      ],
      "observed": [
        1,
        2
      ],
      "tolerance": 1e-8
    }
  ]
}
```

Selected expected result fields:

```json
{
  "/records/0/predictions": [
    1,
    2
  ],
  "/records/0/maximumAbsoluteResidual": 0,
  "/records/0/rootMeanSquareResidual": 0,
  "/records/0/exceedanceCount": 0
}
```

## SSA Function Artifact Consistency Report

Service ID: `ssa-function-artifact-consistency-report`. USD 9.00 per job.

Review an entire normalized SSA function for block and value references, dominance, phi predecessor coverage, instruction placement and return contracts. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ssa-function-artifact-consistency-report) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "entry": "entry",
    "returnType": "i32",
    "parameters": [
      {
        "name": "p",
        "type": "i32"
      }
    ],
    "blocks": [
      {
        "name": "entry",
        "successors": [],
        "instructions": [
          {
            "name": "x",
            "opcode": "add",
            "type": "i32",
            "uses": [
              "p",
              "p"
            ],
            "incoming": []
          },
          {
            "name": "",
            "opcode": "ret",
            "type": "i64",
            "uses": [
              "x"
            ],
            "incoming": []
          }
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 2,
  "/issues/0": "return signature mismatch: entry",
  "/evidence/0": "blocks: 1"
}
```

## Object Link Layout and Resolution Report

Service ID: `object-link-layout-and-resolution-report`. USD 9.00 per job.

Review normalized object sections, definitions and relocation writes as one link-plan artifact, including section spans, strong-symbol ambiguity, unresolved references and overlapping writes. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=object-link-layout-and-resolution-report) · [Technical reference](https://refspecs.linuxfoundation.org/elf/gabi4+/ch4.reloc.html)

Example input:

```json
{
  "data": {
    "sections": [
      {
        "name": "text",
        "bytes": 8,
        "alignment": 4
      }
    ],
    "symbols": [
      {
        "name": "main",
        "section": "text",
        "offset": 0,
        "size": 8,
        "strong": true
      }
    ],
    "relocations": [
      {
        "section": "text",
        "offset": 6,
        "width": 4,
        "target": "main"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "relocation outside section: 0",
  "/evidence/2": "relocations: 1"
}
```

## Typed Stack Control Flow Verification Report

Service ID: `typed-stack-control-flow-verification-report`. USD 9.00 per job.

Verify a normalized typed stack function across all reachable blocks, preserving stack-height and type-merge evidence, underflow, branch conditions and return obligations. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=typed-stack-control-flow-verification-report) · [Technical reference](https://mlir.llvm.org/docs/LangRef/)

Example input:

```json
{
  "data": {
    "entry": "a",
    "returnType": "i32",
    "blocks": [
      {
        "name": "a",
        "successors": [],
        "instructions": [
          {
            "opcode": "ret",
            "type": "i32"
          }
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "return stack differs: a",
  "/evidence/0": "reachable blocks: 1"
}
```

## Grammar Compiler Readiness Report

Service ID: `grammar-compiler-readiness-report`. USD 9.00 per job.

Review a whole finite grammar for symbol partition, unreachable and unproductive rules, nullable left-corner recursion and duplicate productions, with derived productivity and nullability evidence. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=grammar-compiler-readiness-report) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "terminals": [
      "a"
    ],
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "a"
        ]
      },
      {
        "lhs": "A",
        "rhs": [
          "A"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 3,
  "/issues/0": "unreachable nonterminal: A",
  "/evidence/1": "productive: S"
}
```

## Register Assignment Preservation Report

Service ID: `register-assignment-preservation-report`. USD 9.00 per job.

Review an allocator artifact for overlapping live intervals, register width, spill placement, physical-register existence and values live across declared caller-clobber positions. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=register-assignment-preservation-report) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "registers": [
      {
        "name": "r",
        "bits": 64,
        "callerClobbered": true
      }
    ],
    "values": [
      {
        "name": "x",
        "bits": 32,
        "start": 0,
        "end": 4,
        "register": "r",
        "spilled": false
      }
    ],
    "calls": [
      2
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "caller-clobbered live value: x",
  "/evidence/0": "values: 1"
}
```

## Ninja Build Artifact Graph Report

Service ID: `ninja-build-artifact-graph-report`. USD 9.00 per job.

Reconstruct a normalized Ninja-style build artifact graph from source and action inputs, reviewing output ownership, input availability, cycles and requested target production. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ninja-build-artifact-graph-report) · [Technical reference](https://ninja-build.org/manual.html)

Example input:

```json
{
  "data": {
    "sources": [],
    "actions": [
      {
        "name": "compile",
        "inputs": [
          "a.c"
        ],
        "orderOnly": [],
        "outputs": [
          "a.o"
        ]
      }
    ],
    "targets": [
      "a.o"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "unavailable action input: compile / a.c",
  "/evidence/1": "generated artifacts: 1"
}
```

## CMake Exported Compile Interface Report

Service ID: `cmake-consumer-interface-closure-report`. USD 9.00 per job.

Compute a normalized target exported compile usage interface through PUBLIC and INTERFACE links, reviewing unknown targets, omitted dependencies and conflicting macro values. Generator expressions, static link-only PRIVATE propagation and link order are excluded. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cmake-consumer-interface-closure-report) · [Technical reference](https://cmake.org/cmake/help/latest/manual/cmake-buildsystem.7.html)

Example input:

```json
{
  "data": {
    "targets": [
      {
        "name": "app",
        "interfaceDefinitions": []
      },
      {
        "name": "lib",
        "interfaceDefinitions": [
          "FEATURE=1"
        ]
      }
    ],
    "links": [
      {
        "from": "app",
        "to": "lib",
        "visibility": "PUBLIC"
      }
    ],
    "consumer": "app",
    "recordedDependencies": [
      "lib"
    ],
    "recordedDefinitions": []
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "missing interface definition: FEATURE=1",
  "/evidence/0": "dependencies: lib"
}
```

## Cargo Additive Feature Activation Report

Service ID: `cargo-additive-feature-activation-report`. USD 9.00 per job.

Resolve a package additive feature activation closure from explicit requests and optional defaults, including dep-prefixed optional dependencies, and reconcile recorded activation sets. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cargo-additive-feature-activation-report) · [Technical reference](https://doc.rust-lang.org/cargo/reference/features.html)

Example input:

```json
{
  "data": {
    "features": [
      {
        "name": "a",
        "enables": [
          "b"
        ]
      },
      {
        "name": "b",
        "enables": [
          "dep:x"
        ]
      }
    ],
    "optionalDependencies": [
      "x"
    ],
    "requested": [
      "a"
    ],
    "defaultFeatures": [],
    "useDefault": false,
    "recordedFeatures": [
      "a",
      "b"
    ],
    "recordedDependencies": []
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "missing optional dependency activation: x",
  "/evidence/0": "features: a,b"
}
```

## Python Wheel Install Inventory Report

Service ID: `python-wheel-install-inventory-report`. USD 9.00 per job.

Review supplied wheel member and RECORD metadata inventories, required dist-info members, path containment, byte-size and declared-digest equality, and entry-point module presence; digest bytes are not independently hashed. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=python-wheel-install-inventory-report) · [Technical reference](https://packaging.python.org/en/latest/specifications/)

Example input:

```json
{
  "data": {
    "distribution": "demo",
    "version": "1.0",
    "files": [
      {
        "path": "demo.py",
        "bytes": 3,
        "sha256": "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"
      },
      {
        "path": "demo-1.0.dist-info/METADATA",
        "bytes": 1,
        "sha256": "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"
      },
      {
        "path": "demo-1.0.dist-info/WHEEL",
        "bytes": 1,
        "sha256": "bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb"
      },
      {
        "path": "demo-1.0.dist-info/RECORD",
        "bytes": 0,
        "sha256": ""
      }
    ],
    "record": [
      {
        "path": "demo.py",
        "bytes": 3,
        "sha256": "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"
      },
      {
        "path": "demo-1.0.dist-info/METADATA",
        "bytes": 1,
        "sha256": "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"
      },
      {
        "path": "demo-1.0.dist-info/WHEEL",
        "bytes": 1,
        "sha256": "bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb"
      },
      {
        "path": "demo-1.0.dist-info/RECORD",
        "bytes": 0,
        "sha256": ""
      }
    ],
    "entrypoints": [
      {
        "name": "demo",
        "targetPath": "missing.py"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "entry point module absent: demo",
  "/evidence/0": "archive members: 4"
}
```

## NPM Published Package Surface Report

Service ID: `npm-published-package-surface-report`. USD 9.00 per job.

Review normalized resolved export, executable and type-entry targets against a package archive inventory, including containment, duplicate public names and case-folded extraction collisions. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=npm-published-package-surface-report) · [Technical reference](https://docs.npmjs.com/cli/v11/configuring-npm/package-json)

Example input:

```json
{
  "data": {
    "files": [
      "lib/a.js",
      "lib/a.d.ts"
    ],
    "exports": [
      {
        "subpath": ".",
        "target": "./lib/missing.js"
      }
    ],
    "bins": [
      {
        "name": "demo",
        "target": "lib/a.js"
      }
    ],
    "types": "lib/a.d.ts"
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "export target absent from archive: .",
  "/evidence/0": "public exports: 1"
}
```

## SQL Dataset Relational Constraint Report

Service ID: `sql-dataset-relational-constraint-report`. USD 9.00 per job.

Rehearse composite uniqueness, SQL null semantics, MATCH SIMPLE or FULL foreign keys and three-valued CHECK results for a supplied relation as one constraint report. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sql-dataset-relational-constraint-report) · [Technical reference](https://www.postgresql.org/docs/current/ddl-constraints.html)

Example input:

```json
{
  "data": {
    "columns": [
      "id",
      "parent"
    ],
    "nullToken": "NULL",
    "data": [
      [
        "1",
        "a"
      ],
      [
        "1",
        "NULL"
      ]
    ],
    "uniqueConstraints": [
      {
        "name": "pk",
        "columns": [
          0
        ],
        "nullsDistinct": false
      }
    ],
    "foreignKeys": [
      {
        "name": "fk",
        "columns": [
          1
        ],
        "parentRows": [
          [
            "a"
          ]
        ],
        "match": "SIMPLE"
      }
    ],
    "checks": [
      {
        "name": "ok",
        "truth": [
          "true",
          "unknown"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "unique constraint violation: pk / 1",
  "/evidence/0": "relation rows: 2"
}
```

## SQLite Table Btree Hierarchy Report

Service ID: `sqlite-table-btree-hierarchy-report`. USD 9.00 per job.

Review normalized integer-key SQLite table btree pages for ordering, separator ranges, page ownership, balanced leaf depth, reachability and free-list contradictions. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sqlite-table-btree-hierarchy-report) · [Technical reference](https://sqlite.org/fileformat2.html)

Example input:

```json
{
  "data": {
    "root": "r",
    "nodes": [
      {
        "name": "r",
        "leaf": false,
        "keys": [
          10
        ],
        "children": [
          "a",
          "b"
        ]
      },
      {
        "name": "a",
        "leaf": true,
        "keys": [
          1,
          11
        ],
        "children": []
      },
      {
        "name": "b",
        "leaf": true,
        "keys": [
          11,
          20
        ],
        "children": []
      }
    ],
    "freePages": []
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "child exceeds inclusive separator: r / 0",
  "/evidence/0": "visited pages: 3"
}
```

## LSM Compaction Snapshot Preservation Report

Service ID: `lsm-compaction-snapshot-preservation-report`. USD 9.00 per job.

Compare every supplied key snapshot before and after a proposed compaction, detecting resurrected tombstoned keys, lost visible values and ambiguous equal-sequence records. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lsm-compaction-snapshot-preservation-report) · [Technical reference](https://github.com/facebook/rocksdb/wiki/Compaction)

Example input:

```json
{
  "data": {
    "before": [
      {
        "key": "x",
        "sequence": 3,
        "tombstone": false,
        "value": "old"
      },
      {
        "key": "x",
        "sequence": 8,
        "tombstone": true,
        "value": ""
      }
    ],
    "after": [
      {
        "key": "x",
        "sequence": 3,
        "tombstone": false,
        "value": "old"
      }
    ],
    "snapshots": [
      8
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "snapshot visibility changed: x / 8",
  "/evidence/0": "keys compared: 1"
}
```

## Transaction Journal Recovery Rehearsal Report

Service ID: `transaction-journal-recovery-rehearsal-report`. USD 9.00 per job.

Replay explicit begin, put, delete, commit and abort records into a supplied key-value state, comparing recovered values and retaining illegal transaction lifecycle and uncommitted-write evidence. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=transaction-journal-recovery-rehearsal-report) · [Technical reference](https://www.postgresql.org/docs/current/wal-intro.html)

Example input:

```json
{
  "data": {
    "initial": [
      {
        "key": "x",
        "value": "old"
      }
    ],
    "events": [
      {
        "transaction": "t",
        "operation": "begin",
        "key": "",
        "value": ""
      },
      {
        "transaction": "t",
        "operation": "put",
        "key": "x",
        "value": "new"
      },
      {
        "transaction": "t",
        "operation": "abort",
        "key": "",
        "value": ""
      }
    ],
    "recorded": [
      {
        "key": "x",
        "value": "new"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "recovered key-value state differs: x",
  "/evidence/1": "aborted transactions: 1"
}
```

## MVCC Snapshot Version Reconciliation Report

Service ID: `mvcc-snapshot-version-reconciliation-report`. USD 9.00 per job.

Reconcile supplied committed tuple-version metadata with a snapshot boundary and active transaction set, including duplicate visible key versions and invalid creator/deleter order; wraparound and own writes are excluded. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mvcc-snapshot-version-reconciliation-report) · [Technical reference](https://www.postgresql.org/docs/current/mvcc-intro.html)

Example input:

```json
{
  "data": {
    "snapshotMax": 10,
    "activeTransactions": [
      5
    ],
    "versions": [
      {
        "name": "v1",
        "key": "x",
        "creator": 3,
        "hasDeleter": true,
        "deleter": 5,
        "recordedVisible": false
      },
      {
        "name": "v2",
        "key": "x",
        "creator": 5,
        "hasDeleter": false,
        "deleter": 0,
        "recordedVisible": false
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "recorded tuple visibility differs: v1",
  "/evidence/0": "visible versions: v1"
}
```

## CSS Author Layered Cascade Report

Service ID: `css-author-layered-cascade-report`. USD 9.00 per job.

Resolve a supplied author-origin declaration set through importance, flat layer order, specificity and source order for each property, comparing recorded winners and identifying unknown layers and ambiguous order; animations, inline styles and scopes are excluded. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=css-author-layered-cascade-report) · [Technical reference](https://www.w3.org/TR/css-cascade-5/)

Example input:

```json
{
  "data": {
    "layers": [
      "base",
      "theme"
    ],
    "declarations": [
      {
        "property": "color",
        "value": "red",
        "important": true,
        "layer": "base",
        "specificity": [
          0,
          1,
          0
        ],
        "order": 0
      },
      {
        "property": "color",
        "value": "blue",
        "important": true,
        "layer": "theme",
        "specificity": [
          1,
          0,
          0
        ],
        "order": 1
      }
    ],
    "recorded": [
      {
        "property": "color",
        "value": "blue"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "recorded cascaded value differs: color",
  "/evidence/0": "computed winners: color=red"
}
```

## XML Namespace Document Consistency Report

Service ID: `xml-namespace-document-consistency-report`. USD 9.00 per job.

Resolve namespace scopes across an entire normalized XML element tree, reviewing undeclared prefixes, reserved namespace bindings, duplicate namespace declarations and expanded-attribute collisions. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=xml-namespace-document-consistency-report) · [Technical reference](https://www.w3.org/TR/xml-names/)

Example input:

```json
{
  "data": {
    "elements": [
      {
        "parent": -1,
        "qname": "p:root",
        "namespaces": [
          {
            "prefix": "p",
            "uri": "urn:x"
          },
          {
            "prefix": "q",
            "uri": "urn:x"
          }
        ],
        "attributes": [
          {
            "qname": "p:a",
            "value": "1"
          },
          {
            "qname": "q:a",
            "value": "2"
          }
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "duplicate expanded attribute: 0 / urn:x / a",
  "/evidence/0": "element 0: urn:x / root"
}
```

## OpenAPI Operation Routing Contract Report

Service ID: `openapi-operation-routing-contract-report`. USD 9.00 per job.

Review normalized OpenAPI operations together for route-template shape collisions, operation identity, required path bindings, duplicate parameters and response-key contracts. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=openapi-operation-routing-contract-report) · [Technical reference](https://spec.openapis.org/oas/v3.1.1.html)

Example input:

```json
{
  "data": {
    "operations": [
      {
        "path": "/pets/{id}",
        "method": "get",
        "operationId": "pet",
        "parameters": [
          {
            "name": "id",
            "location": "path",
            "required": false
          }
        ],
        "responses": [
          "200",
          "default"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "path parameter is not required: pet / id",
  "/evidence/0": "operations: 1"
}
```

## Source Map V3 Coordinate Artifact Report

Service ID: `source-map-v3-coordinate-artifact-report`. USD 9.00 per job.

Decode Base64 VLQ mappings and review generated and original source coordinate extents, source/name references and segment ordering against supplied line-length inventories. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=source-map-v3-coordinate-artifact-report) · [Technical reference](https://tc39.es/ecma426/)

Example input:

```json
{
  "data": {
    "version": 3,
    "sources": [
      "a.js"
    ],
    "names": [],
    "mappings": "AAAC",
    "generatedLineLengths": [
      1
    ],
    "sourceLineLengths": [
      [
        0
      ]
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "original source column outside line: 0 / 0",
  "/evidence/0": "mapping 0:0 -> 0:0:1"
}
```

## Database History Serializability Report

Service ID: `database-history-serializability-report`. USD 9.00 per job.

Derive a conflict precedence graph and dirty-read/recoverability evidence directly from a supplied ordered read/write/commit/abort history, identifying committed conflict cycles without executing transactions. Reads use the last prior non-aborted write in this single-version model; other isolation models are excluded. Normalized supplied artifact profile only; no source execution, external verification, certification or security endorsement. Integral report quantities must remain exactly representable; unsupported calculation profiles reject before checkout. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=database-history-serializability-report) · [Technical reference](https://www.postgresql.org/docs/current/transaction-iso.html)

Example input:

```json
{
  "data": {
    "events": [
      {
        "transaction": "a",
        "kind": "read",
        "key": "x"
      },
      {
        "transaction": "b",
        "kind": "read",
        "key": "x"
      },
      {
        "transaction": "a",
        "kind": "write",
        "key": "x"
      },
      {
        "transaction": "a",
        "kind": "commit",
        "key": ""
      },
      {
        "transaction": "b",
        "kind": "write",
        "key": "x"
      },
      {
        "transaction": "b",
        "kind": "commit",
        "key": ""
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/issueCount": 1,
  "/issues/0": "committed schedule has a conflict cycle: a,b",
  "/evidence/2": "conflict serializable: false"
}
```

## CFG Epsilon Production Elimination

Service ID: `cfg-epsilon-production-elimination`. USD 1.00 per job.

Eliminate nullable symbol occurrences from a bounded CFG, retaining an empty start production when required. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-epsilon-production-elimination) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "A",
          "b"
        ]
      },
      {
        "lhs": "A",
        "rhs": []
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/productionCount": 2
}
```

## CFG Unit Production Elimination

Service ID: `cfg-unit-production-elimination`. USD 1.00 per job.

Replace nonterminal-to-nonterminal unit chains with reachable non-unit productions while preserving original nonterminal names. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-unit-production-elimination) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "A"
        ]
      },
      {
        "lhs": "A",
        "rhs": [
          "a"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/productionCount": 2
}
```

## CFG Direct Left Recursion Removal

Service ID: `cfg-direct-left-recursion-removal`. USD 1.00 per job.

Remove direct left recursion from one explicitly selected nonterminal using a fresh helper symbol; indirect recursion is unchanged. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-direct-left-recursion-removal) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "E",
    "selected": "E",
    "fresh": "Et",
    "productions": [
      {
        "lhs": "E",
        "rhs": [
          "E",
          "+",
          "n"
        ]
      },
      {
        "lhs": "E",
        "rhs": [
          "n"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/productionCount": 3
}
```

## CFG Explicit Prefix Left Factoring

Service ID: `cfg-explicit-prefix-left-factoring`. USD 1.00 per job.

Factor all productions of a selected head beginning with one supplied nonempty token prefix into a fresh helper nonterminal. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-explicit-prefix-left-factoring) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "selected": "S",
    "fresh": "T",
    "prefix": [
      "a"
    ],
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "a",
          "b"
        ]
      },
      {
        "lhs": "S",
        "rhs": [
          "a",
          "c"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/productionCount": 3
}
```

## CFG Shortest Terminal Yield

Service ID: `cfg-shortest-terminal-yield`. USD 1.00 per job.

Compute a shortest terminal token yield by monotone length improvement with lexical tie breaking; unproductive starts are reported explicitly. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-shortest-terminal-yield) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "A",
          "b"
        ]
      },
      {
        "lhs": "A",
        "rhs": [
          "a"
        ]
      },
      {
        "lhs": "A",
        "rhs": []
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/tokens/0": "b",
  "/value/productive": true
}
```

## CFG Bounded Leftmost Derivation Enumeration

Service ID: `cfg-bounded-leftmost-derivation-enumeration`. USD 1.00 per job.

Enumerate distinct terminal token words reachable by leftmost rewriting within a supplied derivation-step budget. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-bounded-leftmost-derivation-enumeration) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "a",
          "S"
        ]
      },
      {
        "lhs": "S",
        "rhs": []
      }
    ],
    "steps": 3
  }
}
```

Selected expected result fields:

```json
{
  "/value/wordCount": 3
}
```

## CFG LR0 Canonical Item Automaton

Service ID: `cfg-lr0-canonical-item-automaton`. USD 1.00 per job.

Construct augmented LR0 closure and goto item sets with deterministic transition ordering. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-lr0-canonical-item-automaton) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "a"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/stateCount": 3
}
```

## CFG SLR Action Conflict Table

Service ID: `cfg-slr-action-conflict-table`. USD 1.00 per job.

Build SLR shift/reduce/accept action cells from LR0 items and FOLLOW sets, preserving conflicting alternatives instead of resolving them. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-slr-action-conflict-table) · [Technical reference](https://www.gnu.org/software/bison/manual/bison.html)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "a"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/conflictCount": 0
}
```

## Operator Table Infix Postfix Compilation

Service ID: `operator-table-infix-postfix-compilation`. USD 1.00 per job.

Compile an explicit infix token sequence to postfix using supplied precedence and associativity; unary operators and implicit multiplication are excluded. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=operator-table-infix-postfix-compilation) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "tokens": [
      "a",
      "+",
      "b",
      "*",
      "c"
    ],
    "operators": [
      {
        "token": "+",
        "precedence": 1,
        "rightAssociative": false
      },
      {
        "token": "*",
        "precedence": 2,
        "rightAssociative": false
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/postfix/3": "*",
  "/value/postfix/4": "+"
}
```

## Deterministic Token L System Rewriting

Service ID: `deterministic-token-lsystem-rewriting`. USD 1.00 per job.

Apply simultaneous deterministic token rewrite rules for a bounded generation count, preserving tokens without rules. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=deterministic-token-lsystem-rewriting) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "axiom": [
      "A"
    ],
    "rules": [
      {
        "symbol": "A",
        "replacement": [
          "A",
          "B"
        ]
      },
      {
        "symbol": "B",
        "replacement": [
          "A"
        ]
      }
    ],
    "generations": 3
  }
}
```

Selected expected result fields:

```json
{
  "/value/tokens/0": "A",
  "/value/tokenCount": 5
}
```

## Right Linear Grammar NFA Construction

Service ID: `right-linear-grammar-nfa-construction`. USD 1.00 per job.

Convert a normalized grammar with epsilon, one-terminal and terminal-plus-nonterminal productions into an NFA. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=right-linear-grammar-nfa-construction) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "a",
          "S"
        ]
      },
      {
        "lhs": "S",
        "rhs": [
          "b"
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/transitionCount": 2,
  "/value/accepting/0": "@FINAL"
}
```

## DFA Reachable Intersection Product

Service ID: `dfa-reachable-intersection-product`. USD 1.00 per job.

Construct only reachable paired states for the intersection of two complete DFAs over the same alphabet. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dfa-reachable-intersection-product) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "left": {
      "states": [
        "s"
      ],
      "alphabet": [
        "a"
      ],
      "start": "s",
      "accepting": [
        "s"
      ],
      "transitions": [
        {
          "from": "s",
          "symbol": "a",
          "to": "s"
        }
      ]
    },
    "right": {
      "states": [
        "t"
      ],
      "alphabet": [
        "a"
      ],
      "start": "t",
      "accepting": [],
      "transitions": [
        {
          "from": "t",
          "symbol": "a",
          "to": "t"
        }
      ]
    }
  }
}
```

Selected expected result fields:

```json
{
  "/value/stateCount": 1,
  "/value/acceptingCount": 0
}
```

## DFA Shortest Synchronizing Word

Service ID: `dfa-shortest-synchronizing-word`. USD 1.00 per job.

Find a shortest reset word mapping every state of a complete DFA to the same state, using bounded subset BFS. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dfa-shortest-synchronizing-word) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "states": [
      "a",
      "b"
    ],
    "alphabet": [
      "x"
    ],
    "start": "a",
    "accepting": [],
    "transitions": [
      {
        "from": "a",
        "symbol": "x",
        "to": "a"
      },
      {
        "from": "b",
        "symbol": "x",
        "to": "a"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/synchronizing": true,
  "/value/word/0": "x"
}
```

## Mealy Transducer Output Trace

Service ID: `mealy-transducer-output-trace`. USD 1.00 per job.

Execute a supplied deterministic edge-output transducer over token inputs, retaining state and output traces. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mealy-transducer-output-trace) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "start": "a",
    "transitions": [
      {
        "from": "a",
        "input": "x",
        "to": "b",
        "output": "1"
      },
      {
        "from": "b",
        "input": "x",
        "to": "a",
        "output": "0"
      }
    ],
    "word": [
      "x",
      "x"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/outputs/1": "0",
  "/value/finalState": "a"
}
```

## Mealy Observational State Partition

Service ID: `mealy-observational-state-partition`. USD 1.00 per job.

Partition complete finite Mealy states by all future output behavior through fixed-point signature refinement. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mealy-observational-state-partition) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "states": [
      "a",
      "b"
    ],
    "alphabet": [
      "x"
    ],
    "transitions": [
      {
        "from": "a",
        "input": "x",
        "to": "a",
        "output": "0"
      },
      {
        "from": "b",
        "input": "x",
        "to": "b",
        "output": "0"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/classCount": 1
}
```

## Sequential Token Transducer Composition

Service ID: `sequential-token-transducer-composition`. USD 1.00 per job.

Compose two deterministic complete token-output transducers by routing each first-stage output token into the second stage, retaining reachable paired states. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=sequential-token-transducer-composition) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "left": {
      "start": "a",
      "transitions": [
        {
          "from": "a",
          "input": "x",
          "to": "a",
          "output": "y"
        }
      ]
    },
    "right": {
      "start": "b",
      "transitions": [
        {
          "from": "b",
          "input": "y",
          "to": "b",
          "output": "z"
        }
      ]
    },
    "alphabet": [
      "x"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/transitions/0/output": "z"
}
```

## Finite Language Minimal Acyclic Automaton

Service ID: `finite-language-minimal-acyclic-automaton`. USD 1.00 per job.

Construct and bottom-up merge equal suffix subtries for a finite supplied token language, preserving empty-word acceptance. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-language-minimal-acyclic-automaton) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "words": [
      [
        "a",
        "x"
      ],
      [
        "b",
        "x"
      ]
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/stateCount": 3
}
```

## CFG CNF Parse Multiplicity

Service ID: `cfg-cnf-parse-multiplicity`. USD 1.00 per job.

Count parse trees exactly for a supplied token string under a strict binary-or-terminal CNF grammar, distinguishing ambiguity from recognition. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-cnf-parse-multiplicity) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "S",
          "S"
        ]
      },
      {
        "lhs": "S",
        "rhs": [
          "a"
        ]
      }
    ],
    "tokens": [
      "a",
      "a",
      "a"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/parseCount": "2"
}
```

## CFG Weighted CNF Best Parse

Service ID: `cfg-weighted-cnf-best-parse`. USD 1.00 per job.

Find a minimum additive-cost parse tree in strict CNF using supplied exact nonnegative rule costs and deterministic first-rule ties. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cfg-weighted-cnf-best-parse) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "start": "S",
    "productions": [
      {
        "lhs": "S",
        "rhs": [
          "A",
          "B"
        ],
        "cost": 2
      },
      {
        "lhs": "A",
        "rhs": [
          "a"
        ],
        "cost": 3
      },
      {
        "lhs": "B",
        "rhs": [
          "b"
        ],
        "cost": 4
      }
    ],
    "tokens": [
      "a",
      "b"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/recognized": true,
  "/value/cost": 9
}
```

## Finite Word Rewrite Critical Overlap Pairs

Service ID: `finite-rewrite-critical-overlap-pairs`. USD 1.00 per job.

Enumerate nonempty proper suffix-prefix overlaps of finite literal rewrite rules and the two immediate divergent reducts; confluence is not inferred. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-rewrite-critical-overlap-pairs) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "rules": [
      {
        "left": "ab",
        "right": "x"
      },
      {
        "left": "bc",
        "right": "y"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/pairCount": 1,
  "/value/pairs/0/word": "abc"
}
```

## Compiler Live Variable Fixed Point

Service ID: `compiler-live-variable-fixed-point`. USD 1.00 per job.

Compute backward may-live IN and OUT variable sets from normalized block USE, DEF and successor sets. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-live-variable-fixed-point) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "entry": "a",
    "blocks": [
      {
        "name": "a",
        "use": [],
        "def": [
          "x"
        ],
        "successors": [
          "b"
        ]
      },
      {
        "name": "b",
        "use": [
          "x"
        ],
        "def": [],
        "successors": []
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/blocks/0/liveOut/0": "x",
  "/value/blocks/0/liveInCount": 0
}
```

## Compiler Reaching Definition Fixed Point

Service ID: `compiler-reaching-definition-fixed-point`. USD 1.00 per job.

Compute forward may-reaching named definition sets from supplied GEN and KILL sets and CFG edges. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-reaching-definition-fixed-point) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "entry": "a",
    "blocks": [
      {
        "name": "a",
        "gen": [
          "x1"
        ],
        "kill": [],
        "successors": [
          "b"
        ]
      },
      {
        "name": "b",
        "gen": [
          "x2"
        ],
        "kill": [
          "x1"
        ],
        "successors": []
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/blocks/1/in/0": "x1",
  "/value/blocks/1/out/0": "x2"
}
```

## Compiler Available Expression Fixed Point

Service ID: `compiler-available-expression-fixed-point`. USD 1.00 per job.

Compute forward must-available expression identifiers by predecessor intersection and block GEN/KILL transfer. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-available-expression-fixed-point) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "entry": "a",
    "blocks": [
      {
        "name": "a",
        "gen": [],
        "kill": [],
        "successors": [
          "b",
          "c"
        ]
      },
      {
        "name": "b",
        "gen": [
          "e"
        ],
        "kill": [],
        "successors": [
          "d"
        ]
      },
      {
        "name": "c",
        "gen": [],
        "kill": [],
        "successors": [
          "d"
        ]
      },
      {
        "name": "d",
        "gen": [],
        "kill": [],
        "successors": []
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/blocks/3/in": []
}
```

## Compiler Dominance Frontier Construction

Service ID: `compiler-dominance-frontier-construction`. USD 1.00 per job.

Compute dominance frontiers for reachable CFG nodes, including loop self-frontiers useful for SSA phi placement. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-dominance-frontier-construction) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "nodes": [
      "a",
      "b",
      "c",
      "d"
    ],
    "entry": "a",
    "edges": [
      {
        "from": "a",
        "to": "b"
      },
      {
        "from": "a",
        "to": "c"
      },
      {
        "from": "b",
        "to": "d"
      },
      {
        "from": "c",
        "to": "d"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/frontiers/1/nodes/0": "d"
}
```

## Compiler Natural Loop Discovery

Service ID: `compiler-natural-loop-discovery`. USD 1.00 per job.

Find dominance-backed CFG back edges and recover each natural loop by reverse predecessor closure. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-natural-loop-discovery) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "nodes": [
      "a",
      "b",
      "c"
    ],
    "entry": "a",
    "edges": [
      {
        "from": "a",
        "to": "b"
      },
      {
        "from": "b",
        "to": "c"
      },
      {
        "from": "c",
        "to": "b"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/loopCount": 1,
  "/value/loops/0/members/0": "b"
}
```

## Compiler Critical Edge Splitting

Service ID: `compiler-critical-edge-splitting`. USD 1.00 per job.

Insert fresh intermediate blocks on edges whose source has multiple successors and target has multiple predecessors. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-critical-edge-splitting) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "nodes": [
      "a",
      "b",
      "c"
    ],
    "entry": "a",
    "edges": [
      {
        "from": "a",
        "to": "b"
      },
      {
        "from": "a",
        "to": "c"
      },
      {
        "from": "b",
        "to": "c"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/splitCount": 1
}
```

## Compiler Parallel Copy Sequentialization

Service ID: `compiler-parallel-copy-sequentialization`. USD 1.00 per job.

Schedule simultaneous register copies into sequential moves, introducing one fresh temporary when breaking cycles. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-parallel-copy-sequentialization) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "copies": [
      {
        "to": "a",
        "from": "b"
      },
      {
        "to": "b",
        "from": "a"
      }
    ],
    "temporary": "t"
  }
}
```

Selected expected result fields:

```json
{
  "/value/moveCount": 3
}
```

## Compiler Linear Scan Register Allocation

Service ID: `compiler-linear-scan-register-allocation`. USD 1.00 per job.

Allocate supplied half-open live intervals with expiration and farthest-end spilling under a fixed register set. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-linear-scan-register-allocation) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "registers": [
      "r0"
    ],
    "intervals": [
      {
        "name": "a",
        "start": 0,
        "end": 10
      },
      {
        "name": "b",
        "start": 1,
        "end": 2
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/spilled/0": "a"
}
```

## Compiler Local Value Numbering

Service ID: `compiler-local-value-numbering`. USD 1.00 per job.

Identify equivalent pure binary expressions in a straight-line SSA block, canonicalizing operands only for explicitly commutative operations. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-local-value-numbering) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "parameters": [
      "a",
      "b"
    ],
    "instructions": [
      {
        "name": "x",
        "opcode": "add",
        "left": "a",
        "right": "b",
        "commutative": true
      },
      {
        "name": "y",
        "opcode": "add",
        "left": "b",
        "right": "a",
        "commutative": true
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/replacements/0/name": "y",
  "/value/replacements/0/equivalent": "x"
}
```

## Compiler Straight Line Dead Store Elimination

Service ID: `compiler-straight-line-dead-store-elimination`. USD 1.00 per job.

Remove earlier exact-address stores overwritten before any matching read or declared memory barrier; aliasing addresses must be supplied identically. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-straight-line-dead-store-elimination) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "operations": [
      {
        "kind": "store",
        "address": "a",
        "value": "1"
      },
      {
        "kind": "store",
        "address": "a",
        "value": "2"
      },
      {
        "kind": "load",
        "address": "a",
        "value": ""
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/removed/0": 0
}
```

## Compiler Integer Stack Bytecode Evaluation

Service ID: `compiler-integer-stack-bytecode-evaluation`. USD 1.00 per job.

Evaluate a bounded integer stack language with checked add, subtract, multiply, exact division, dup and swap; no host code is executed. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-integer-stack-bytecode-evaluation) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "instructions": [
      {
        "opcode": "push",
        "operand": 6
      },
      {
        "opcode": "push",
        "operand": 7
      },
      {
        "opcode": "mul",
        "operand": 0
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/stack/0": 42
}
```

## Compiler DAG Expression Instruction Selection

Service ID: `compiler-dag-expression-instruction-selection`. USD 1.00 per job.

Select a minimum additive-cost instruction cover for a supplied expression tree using explicit leaf, binary and fused multiply-add costs. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-dag-expression-instruction-selection) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "postfix": [
      "a",
      "b",
      "*",
      "c",
      "+"
    ],
    "leafCost": 0,
    "binaryCost": 2,
    "fmaCost": 3
  }
}
```

Selected expected result fields:

```json
{
  "/value/cost": 3,
  "/value/selected/0": "fma"
}
```

## Compiler Structure Field Layout

Service ID: `compiler-structure-field-layout`. USD 1.00 per job.

Lay out supplied structure fields with explicit byte sizes and power-of-two alignments, including internal and tail padding; bitfields and platform ABI inference are excluded. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-structure-field-layout) · [Technical reference](https://itanium-cxx-abi.github.io/cxx-abi/abi.html)

Example input:

```json
{
  "data": {
    "fields": [
      {
        "name": "a",
        "size": 1,
        "alignment": 1
      },
      {
        "name": "b",
        "size": 4,
        "alignment": 4
      }
    ],
    "minimumAlignment": 1
  }
}
```

Selected expected result fields:

```json
{
  "/value/size": 8,
  "/value/fields/1/offset": 4
}
```

## Compiler Sethi Ullman Register Number

Service ID: `compiler-sethi-ullman-register-number`. USD 1.00 per job.

Compute expression-tree register demand and child evaluation order under the classic binary-register Sethi Ullman model. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-sethi-ullman-register-number) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "postfix": [
      "a",
      "b",
      "+",
      "c",
      "d",
      "+",
      "*"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/registers": 3
}
```

## Lambda Free Variable and Binding Index

Service ID: `lambda-free-variable-and-binding-index`. USD 1.00 per job.

Convert a finite named lambda AST to a de Bruijn indexed expression while separately preserving free variable names. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lambda-free-variable-and-binding-index) · [Technical reference](https://plato.stanford.edu/entries/lambda-calculus/)

Example input:

```json
{
  "data": {
    "nodes": [
      {
        "kind": "var",
        "name": "x",
        "left": 0,
        "right": 0
      },
      {
        "kind": "lam",
        "name": "x",
        "left": 0,
        "right": 0
      }
    ],
    "root": 1
  }
}
```

Selected expected result fields:

```json
{
  "/value/indexed": "(lambda #0)"
}
```

## Lambda Capture Avoiding Substitution

Service ID: `lambda-capture-avoiding-substitution`. USD 1.00 per job.

Substitute one free variable with a supplied lambda term, renaming conflicting binders deterministically. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lambda-capture-avoiding-substitution) · [Technical reference](https://plato.stanford.edu/entries/lambda-calculus/)

Example input:

```json
{
  "data": {
    "term": {
      "nodes": [
        {
          "kind": "var",
          "name": "x",
          "left": 0,
          "right": 0
        },
        {
          "kind": "lam",
          "name": "y",
          "left": 0,
          "right": 0
        }
      ],
      "root": 1
    },
    "variable": "x",
    "replacement": {
      "nodes": [
        {
          "kind": "var",
          "name": "y",
          "left": 0,
          "right": 0
        }
      ],
      "root": 0
    }
  }
}
```

Selected expected result fields:

```json
{
  "/value/term": "(lambda y_0 y)"
}
```

## Lambda Bounded Normal Order Beta Reduction

Service ID: `lambda-bounded-normal-order-beta-reduction`. USD 1.00 per job.

Perform leftmost outermost beta reduction with capture-avoiding substitution and a strict step/output budget; report residual reducibility honestly. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lambda-bounded-normal-order-beta-reduction) · [Technical reference](https://plato.stanford.edu/entries/lambda-calculus/)

Example input:

```json
{
  "data": {
    "term": {
      "nodes": [
        {
          "kind": "var",
          "name": "x",
          "left": 0,
          "right": 0
        },
        {
          "kind": "lam",
          "name": "x",
          "left": 0,
          "right": 0
        },
        {
          "kind": "var",
          "name": "y",
          "left": 0,
          "right": 0
        },
        {
          "kind": "app",
          "name": "",
          "left": 1,
          "right": 2
        }
      ],
      "root": 3
    },
    "steps": 2
  }
}
```

Selected expected result fields:

```json
{
  "/value/term": "y",
  "/value/stepsUsed": 1
}
```

## Lambda SKI Bracket Abstraction

Service ID: `lambda-ski-bracket-abstraction`. USD 1.00 per job.

Compile a named lambda term into the S, K and I combinator basis with explicit application structure and free-variable preservation. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=lambda-ski-bracket-abstraction) · [Technical reference](https://plato.stanford.edu/entries/logic-combinatory/)

Example input:

```json
{
  "data": {
    "nodes": [
      {
        "kind": "var",
        "name": "x",
        "left": 0,
        "right": 0
      },
      {
        "kind": "lam",
        "name": "x",
        "left": 0,
        "right": 0
      }
    ],
    "root": 1
  }
}
```

Selected expected result fields:

```json
{
  "/value/combinator": "I"
}
```

## Compiler Tail Call Cycle Classification

Service ID: `compiler-tail-call-cycle-classification`. USD 1.00 per job.

Classify recursive call-graph components by whether all internal recursive edges are explicitly recorded as tail calls. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-tail-call-cycle-classification) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "functions": [
      "a",
      "b"
    ],
    "calls": [
      {
        "from": "a",
        "to": "b",
        "tail": true
      },
      {
        "from": "b",
        "to": "a",
        "tail": false
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/components/0/tailOnly": false
}
```

## Compiler Stack Frame Slot Coalescing

Service ID: `compiler-stack-frame-slot-coalescing`. USD 1.00 per job.

Greedily coalesce equal-size equally-aligned stack slots with nonoverlapping half-open lifetimes, returning physical slot offsets and frame size. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=compiler-stack-frame-slot-coalescing) · [Technical reference](https://llvm.org/docs/LangRef.html)

Example input:

```json
{
  "data": {
    "slots": [
      {
        "name": "a",
        "start": 0,
        "end": 2,
        "size": 4,
        "alignment": 4
      },
      {
        "name": "b",
        "start": 2,
        "end": 4,
        "size": 4,
        "alignment": 4
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/frameBytes": 4,
  "/value/assignments/1/offset": 0
}
```

## Minimum Palindromic Partition Witness

Service ID: `minimum-palindromic-partition-witness`. USD 1.00 per job.

Construct a minimum-cardinality partition of a Unicode scalar string into nonempty palindromes, including scalar cut boundaries and the exact number of optimal partitions as decimal text. Ties choose the earliest first cut recursively; length at most 96. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=minimum-palindromic-partition-witness) · [Technical reference](https://arxiv.org/abs/1403.2431)

Example input:

```json
{
  "data": {
    "text": "abab"
  }
}
```

Selected expected result fields:

```json
{
  "/value/minimumFactors": 2,
  "/value/factors": [
    "a",
    "bab"
  ],
  "/value/boundaries": [
    0,
    1,
    4
  ],
  "/value/optimalCount": "2"
}
```

## Maximal Periodic String Run Index

Service ID: `maximal-periodic-string-run-index`. USD 1.00 per job.

Enumerate maximal periodic runs with least period and exponent at least two using bounded exact codepoint comparisons. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=maximal-periodic-string-run-index) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "text": "ababab"
  }
}
```

Selected expected result fields:

```json
{
  "/value/runCount": 1,
  "/value/runs/0/period": 2
}
```

## Minimal Unique Substring Index

Service ID: `minimal-unique-substring-index`. USD 1.00 per job.

Enumerate unique codepoint substrings whose proper one-character prefix and suffix are both nonunique or empty. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=minimal-unique-substring-index) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "text": "aba"
  }
}
```

Selected expected result fields:

```json
{
  "/value/substrings/0/text": "b"
}
```

## Shortest Absent Alphabet Word

Service ID: `shortest-absent-alphabet-word`. USD 1.00 per job.

Find the lexicographically first shortest word over an explicit alphabet absent as a contiguous substring. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=shortest-absent-alphabet-word) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "text": "ab",
    "alphabet": [
      "a",
      "b"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/word": "aa"
}
```

## Greedy LZ77 Overlapping Factorization

Service ID: `greedy-lz77-overlapping-factorization`. USD 1.00 per job.

Factor codepoints into literals and longest previous-window matches, explicitly allowing overlapping copies and using nearest-distance ties. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=greedy-lz77-overlapping-factorization) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "text": "aaaaa",
    "window": 8,
    "minimumMatch": 2
  }
}
```

Selected expected result fields:

```json
{
  "/value/tokens/1/length": 4,
  "/value/tokens/1/distance": 1
}
```

## Exact Shortest Superstring Assembly

Service ID: `exact-shortest-superstring-assembly`. USD 1.00 per job.

Find a shortest string containing every supplied string contiguously using exact subset dynamic programming after containment reduction. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=exact-shortest-superstring-assembly) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "strings": [
      "ab",
      "bc",
      "ca"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/length": 4
}
```

## Subsequence Distinct Embedding Count

Service ID: `subsequence-distinct-embedding-count`. USD 1.00 per job.

Count distinct strictly increasing codepoint-position embeddings of one pattern as a subsequence of supplied text, using exact integer arithmetic. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=subsequence-distinct-embedding-count) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "text": "rabbbit",
    "pattern": "rabbit"
  }
}
```

Selected expected result fields:

```json
{
  "/value/count": "3"
}
```

## Minimum Window Subsequence Embedding

Service ID: `minimum-window-subsequence-embedding`. USD 1.00 per job.

Find the shortest contiguous codepoint window containing the supplied pattern as a subsequence, with earliest-start ties. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=minimum-window-subsequence-embedding) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "text": "abcdebdde",
    "pattern": "bde"
  }
}
```

Selected expected result fields:

```json
{
  "/value/text": "bcde",
  "/value/start": 1
}
```

## Palindromic Tree Distinct Substring Index

Service ID: `palindromic-tree-distinct-substring-index`. USD 1.00 per job.

Construct distinct palindromic substring nodes, occurrence counts and longest proper palindromic suffix links from supplied codepoints. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=palindromic-tree-distinct-substring-index) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "text": "ababa"
  }
}
```

Selected expected result fields:

```json
{
  "/value/nodeCount": 5
}
```

## String Suffix Prefix Overlap Network

Service ID: `string-suffix-prefix-overlap-network`. USD 1.00 per job.

Compute longest proper suffix-prefix overlaps between distinct supplied strings, returning explicit assembly edges and overlap labels. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=string-suffix-prefix-overlap-network) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "strings": [
      "abcd",
      "cdef"
    ],
    "minimumOverlap": 1
  }
}
```

Selected expected result fields:

```json
{
  "/value/edges/0/overlap": 2
}
```

## Ordered Rooted Tree Edit Distance

Service ID: `ordered-rooted-tree-edit-distance`. USD 1.00 per job.

Compute exact ordered tree edit distance with unit insert, delete and relabel costs using recursive forest dynamic programming; trees are bounded to twelve nodes. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ordered-rooted-tree-edit-distance) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "left": {
      "nodes": [
        {
          "label": "a",
          "children": [
            1
          ]
        },
        {
          "label": "b",
          "children": []
        }
      ],
      "root": 0
    },
    "right": {
      "nodes": [
        {
          "label": "a",
          "children": [
            1
          ]
        },
        {
          "label": "c",
          "children": []
        }
      ],
      "root": 0
    }
  }
}
```

Selected expected result fields:

```json
{
  "/value/distance": 1
}
```

## Ordered Tree Wildcard Pattern Match

Service ID: `ordered-tree-wildcard-pattern-match`. USD 1.00 per job.

Find exact ordered subtree pattern occurrences with an explicit whole-subtree wildcard label, preserving child order for ordinary labels. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ordered-tree-wildcard-pattern-match) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "tree": {
      "nodes": [
        {
          "label": "a",
          "children": [
            1
          ]
        },
        {
          "label": "b",
          "children": []
        }
      ],
      "root": 0
    },
    "pattern": {
      "nodes": [
        {
          "label": "a",
          "children": [
            1
          ]
        },
        {
          "label": "*",
          "children": []
        }
      ],
      "root": 0
    },
    "wildcard": "*"
  }
}
```

Selected expected result fields:

```json
{
  "/value/matches/0": 0
}
```

## Cartesian Min Tree Construction

Service ID: `cartesian-min-tree-construction`. USD 1.00 per job.

Construct the stable min Cartesian tree of an integer sequence, preserving in-order positions and choosing the earlier index for equal minima. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=cartesian-min-tree-construction) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "values": [
      3,
      1,
      2
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/root": 1,
  "/value/nodes/1/left": 0
}
```

## Patricia Radix Trie Construction

Service ID: `patricia-radix-trie-construction`. USD 1.00 per job.

Build a compressed prefix radix trie from distinct supplied codepoint words, retaining terminal nodes within shared paths. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=patricia-radix-trie-construction) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "words": [
      "romane",
      "romanus",
      "romulus"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/nodeCount": 6
}
```

## Splay Search Tree Access Trace

Service ID: `splay-search-tree-access-trace`. USD 1.00 per job.

Insert distinct integer keys and perform bottom-up splay searches, recording each accessed root and final tree structure. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=splay-search-tree-access-trace) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "insert": [
      1,
      2,
      3
    ],
    "access": [
      1
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/root": 1
}
```

## Left Leaning Red Black Insertion Trace

Service ID: `left-leaning-red-black-insertion-trace`. USD 1.00 per job.

Insert integer keys into a left-leaning red-black tree with color flips and rotations, returning colored nodes and root traces. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=left-leaning-red-black-insertion-trace) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "keys": [
      3,
      2,
      1
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/root": 2
}
```

## Pairing Heap Two Pass Delete Trace

Service ID: `pairing-heap-two-pass-delete-trace`. USD 1.00 per job.

Replay integer insert and delete-min operations on a pairing heap with pairwise first-pass melding and right-to-left second pass. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pairing-heap-two-pass-delete-trace) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "operations": [
      {
        "kind": "insert",
        "value": 3
      },
      {
        "kind": "insert",
        "value": 1
      },
      {
        "kind": "insert",
        "value": 2
      },
      {
        "kind": "pop",
        "value": 0
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/removed/0": 1,
  "/value/minimum": 2
}
```

## Dictionary Levenshtein Trie Search

Service ID: `dictionary-levenshtein-trie-search`. USD 1.00 per job.

Search a supplied token dictionary within a small Levenshtein radius by propagating edit-distance rows through a shared prefix trie. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=dictionary-levenshtein-trie-search) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "words": [
      "cat",
      "bat",
      "dog"
    ],
    "query": "cat",
    "radius": 1
  }
}
```

Selected expected result fields:

```json
{
  "/value/matchCount": 2
}
```

## Positional Inverted Index Phrase Query

Service ID: `positional-inverted-index-phrase-query`. USD 1.00 per job.

Build a supplied token document positional index and return exact phrase occurrences without stemming or linguistic normalization. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=positional-inverted-index-phrase-query) · [Technical reference](https://xlinux.nist.gov/dads/)

Example input:

```json
{
  "data": {
    "documents": [
      {
        "name": "d",
        "tokens": [
          "a",
          "b",
          "a",
          "b"
        ]
      }
    ],
    "phrase": [
      "a",
      "b"
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/matchCount": 2,
  "/value/matches/1/start": 2
}
```

## Minimum String Attractor Exact

Service ID: `minimum-string-attractor-exact`. USD 1.00 per job.

Find a smallest codepoint-position set intersecting at least one occurrence of every distinct nonempty substring, using exhaustive bounded set cover. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=minimum-string-attractor-exact) · [Technical reference](https://arxiv.org/abs/1710.10964)

Example input:

```json
{
  "data": {
    "text": "aba"
  }
}
```

Selected expected result fields:

```json
{
  "/value/size": 2
}
```

## Ranked Tree Automaton Minimum Witness

Service ID: `ranked-tree-automaton-minimum-witness`. USD 1.00 per job.

Find a minimum-node accepted finite ranked tree in a supplied bottom-up tree automaton, retaining a postorder state-annotated witness; trees above 128 nodes reject and empty languages return an explicit null root. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ranked-tree-automaton-minimum-witness) · [Technical reference](https://jacquema.gitlabpages.inria.fr/files/tata.pdf)

Example input:

```json
{
  "data": {
    "states": [
      "leaf",
      "pair"
    ],
    "accepting": [
      "pair"
    ],
    "alphabet": [
      {
        "symbol": "a",
        "arity": 0
      },
      {
        "symbol": "f",
        "arity": 2
      }
    ],
    "transitions": [
      {
        "symbol": "a",
        "children": [],
        "parent": "leaf"
      },
      {
        "symbol": "f",
        "children": [
          "leaf",
          "leaf"
        ],
        "parent": "pair"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/nonempty": true,
  "/value/nodeCount": 3,
  "/value/root": 2
}
```

## Boolean Algebraic Normal Form Transform

Service ID: `boolean-algebraic-normal-form-transform`. USD 1.00 per job.

Compute exact GF(2) algebraic-normal-form coefficients from a complete Boolean truth table using the subset Mobius transform. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=boolean-algebraic-normal-form-transform) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "variables": 2,
    "truth": [
      0,
      1,
      1,
      1
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/monomials/2/mask": 3
}
```

## Quine McCluskey Prime Implicant Enumeration

Service ID: `quine-mccluskey-prime-implicant-enumeration`. USD 1.00 per job.

Enumerate all prime Boolean implicant cubes from supplied on-set and optional dont-care minterms. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=quine-mccluskey-prime-implicant-enumeration) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "variables": 3,
    "minterms": [
      1,
      3
    ],
    "dontCare": []
  }
}
```

Selected expected result fields:

```json
{
  "/value/implicants/0": "0-1"
}
```

## Boolean Minimum Two Level SOP Cover

Service ID: `boolean-minimum-two-level-sop-cover`. USD 1.00 per job.

Select an exact minimum prime-implicant cover by implicant count then literal count, preserving explicit on-set coverage. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=boolean-minimum-two-level-sop-cover) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "variables": 3,
    "minterms": [
      1,
      3
    ],
    "dontCare": []
  }
}
```

Selected expected result fields:

```json
{
  "/value/implicants/0": "0-1",
  "/value/literalCount": 2
}
```

## Horn Clause Least Model Inference

Service ID: `horn-clause-least-model-inference`. USD 1.00 per job.

Compute the least model of finite definite Horn implications and identify violated headless constraints. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=horn-clause-least-model-inference) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "facts": [
      "a"
    ],
    "rules": [
      {
        "premises": [
          "a"
        ],
        "head": "b"
      },
      {
        "premises": [
          "b"
        ],
        "head": "c"
      }
    ],
    "constraints": [
      [
        "c"
      ]
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/satisfiable": false,
  "/value/model/2": "c"
}
```

## CTL Finite Kripke Model Checking

Service ID: `ctl-finite-kripke-model-checking`. USD 1.00 per job.

Evaluate normalized CTL atom, Boolean, EX, AX, EF, AF, EG, AG, EU and AU formulas on a supplied total finite Kripke graph. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ctl-finite-kripke-model-checking) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "states": [
      {
        "name": "a",
        "labels": [],
        "successors": [
          "b"
        ]
      },
      {
        "name": "b",
        "labels": [
          "p"
        ],
        "successors": [
          "b"
        ]
      }
    ],
    "formulas": [
      {
        "op": "atom",
        "atom": "p",
        "left": 0,
        "right": 0
      },
      {
        "op": "AF",
        "atom": "",
        "left": 0,
        "right": 0
      }
    ],
    "root": 1
  }
}
```

Selected expected result fields:

```json
{
  "/value/satisfying/0": "a",
  "/value/satisfying/1": "b"
}
```

## Buchi Accepting Lasso Witness

Service ID: `buchi-accepting-lasso-witness`. USD 1.00 per job.

Find a reachable accepting state with a nonempty return cycle and emit a finite prefix-plus-cycle witness for an infinite accepted run. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=buchi-accepting-lasso-witness) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "states": [
      "a",
      "b"
    ],
    "start": "a",
    "accepting": [
      "b"
    ],
    "edges": [
      {
        "from": "a",
        "to": "b"
      },
      {
        "from": "b",
        "to": "b"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/nonempty": true,
  "/value/cycle/0": "b"
}
```

## Zero Suppressed Decision Diagram Family

Service ID: `zero-suppressed-decision-diagram-family`. USD 1.00 per job.

Build a reduced ordered ZDD for an explicitly enumerated finite set family using zero suppression and unique node interning. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=zero-suppressed-decision-diagram-family) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "variables": [
      "a",
      "b"
    ],
    "family": [
      [
        "a"
      ],
      [
        "b"
      ]
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/familyCount": 2
}
```

## Finite Transformation Semigroup Closure

Service ID: `finite-transformation-semigroup-closure`. USD 1.00 per job.

Enumerate the finite transformation semigroup generated by supplied total functions, retaining shortest generator words for discovered maps. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-transformation-semigroup-closure) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "degree": 2,
    "generators": [
      [
        1,
        0
      ]
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/elementCount": 2
}
```

## Finite Cayley Group Table Analysis

Service ID: `finite-cayley-group-table-analysis`. USD 1.00 per job.

Analyze a complete finite operation table for associativity, identity, inverses and commutativity, returning witnesses when group axioms fail. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-cayley-group-table-analysis) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "table": [
      [
        0,
        1
      ],
      [
        1,
        0
      ]
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/group": true,
  "/value/identity": 0
}
```

## Permutation Group Point Stabilizer

Service ID: `permutation-group-point-stabilizer`. USD 1.00 per job.

Enumerate a bounded permutation group from generators and return its point orbit and the exact point stabilizer subgroup. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=permutation-group-point-stabilizer) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "degree": 3,
    "generators": [
      [
        1,
        2,
        0
      ],
      [
        1,
        0,
        2
      ]
    ],
    "point": 0
  }
}
```

Selected expected result fields:

```json
{
  "/value/groupOrder": 6,
  "/value/stabilizerOrder": 2
}
```

## Free Group Reduced Word Normal Form

Service ID: `free-group-reduced-word-normal-form`. USD 1.00 per job.

Reduce a supplied signed-generator word by adjacent inverse cancellation and report its cyclically reduced core and conjugating prefix. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=free-group-reduced-word-normal-form) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "word": [
      1,
      2,
      -2,
      -1,
      3
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/reduced/0": 3,
  "/value/reducedLength": 1
}
```

## Finite Relation Equivalence Quotient

Service ID: `finite-relation-equivalence-quotient`. USD 1.00 per job.

Compute the least equivalence relation containing supplied pairs and return canonical classes and the induced quotient map. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-relation-equivalence-quotient) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "elements": [
      "a",
      "b",
      "c"
    ],
    "pairs": [
      {
        "from": "a",
        "to": "b"
      },
      {
        "from": "b",
        "to": "c"
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/classCount": 1
}
```

## Ground Term Congruence Closure

Service ID: `ground-term-congruence-closure`. USD 1.00 per job.

Compute congruence closure of supplied equations over finite acyclic ground-term DAG nodes, propagating equality through equal function applications. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ground-term-congruence-closure) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "terms": [
      {
        "symbol": "a",
        "args": []
      },
      {
        "symbol": "b",
        "args": []
      },
      {
        "symbol": "f",
        "args": [
          0
        ]
      },
      {
        "symbol": "f",
        "args": [
          1
        ]
      }
    ],
    "equations": [
      {
        "left": 0,
        "right": 1
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/classes/1/1": 3,
  "/value/classCount": 2
}
```

## Boolean Truth Table Existential Quantification

Service ID: `boolean-truth-table-existential-quantification`. USD 1.00 per job.

Eliminate selected Boolean variables by existentially OR-ing compatible truth-table rows, returning the projected Boolean function. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=boolean-truth-table-existential-quantification) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "variables": 2,
    "truth": [
      0,
      1,
      1,
      0
    ],
    "eliminate": [
      1
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/truth/0": 1,
  "/value/truth/1": 1
}
```

## Petri Minimal Nonnegative Place Invariants

Service ID: `petri-minimal-nonnegative-place-invariants`. USD 1.00 per job.

Enumerate bounded nonzero nonnegative integer place invariants, retaining componentwise-minimal vectors satisfying the exact transition incidence equations. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=petri-minimal-nonnegative-place-invariants) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "incidence": [
      [
        -1,
        1
      ]
    ],
    "maximumCoefficient": 2
  }
}
```

Selected expected result fields:

```json
{
  "/value/invariants/0/0": 1,
  "/value/invariants/0/1": 1
}
```

## Petri Coverability Karp Miller Tree

Service ID: `petri-coverability-karp-miller-tree`. USD 1.00 per job.

Construct a bounded Karp Miller coverability tree for an ordinary Petri net, using omega acceleration against ancestors and explicit truncation rejection. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=petri-coverability-karp-miller-tree) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "initial": [
      1
    ],
    "transitions": [
      {
        "consume": [
          1
        ],
        "produce": [
          2
        ]
      }
    ]
  }
}
```

Selected expected result fields:

```json
{
  "/value/unbounded": true
}
```

## Finite Elementary Cellular Automaton Trace

Service ID: `finite-elementary-cellular-automaton-trace`. USD 1.00 per job.

Evolve a finite binary one-dimensional elementary cellular automaton with an explicit Wolfram rule and fixed-zero or periodic boundaries. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-elementary-cellular-automaton-trace) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "initial": [
      0,
      0,
      1,
      0,
      0
    ],
    "rule": 90,
    "steps": 1,
    "periodic": false
  }
}
```

Selected expected result fields:

```json
{
  "/value/rows/1/1": 1,
  "/value/rows/1/3": 1
}
```

## Finite Tag System Deletion Rewrite Trace

Service ID: `finite-tag-system-deletion-rewrite-trace`. USD 1.00 per job.

Replay a deterministic tag system that deletes a fixed prefix length and appends the rule selected by the first token, with explicit halt and work limits. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=finite-tag-system-deletion-rewrite-trace) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "word": [
      "a",
      "b"
    ],
    "deletion": 2,
    "rules": [
      {
        "symbol": "a",
        "append": [
          "b",
          "a",
          "a"
        ]
      },
      {
        "symbol": "b",
        "append": [
          "a"
        ]
      }
    ],
    "steps": 1
  }
}
```

Selected expected result fields:

```json
{
  "/value/word/0": "b",
  "/value/wordLength": 3
}
```

## Bounded Post Correspondence Witness Search

Service ID: `bounded-post-correspondence-witness-search`. USD 1.00 per job.

Search a bounded Post correspondence instance for a nonempty tile-index sequence equating top and bottom concatenations, pruning incompatible prefixes. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bounded-post-correspondence-witness-search) · [Technical reference](https://ocw.mit.edu/courses/6-045j-automata-computability-and-complexity-spring-2011/)

Example input:

```json
{
  "data": {
    "tiles": [
      {
        "top": "a",
        "bottom": "ab"
      },
      {
        "top": "ba",
        "bottom": "a"
      }
    ],
    "maximumTiles": 2
  }
}
```

Selected expected result fields:

```json
{
  "/value/found": true,
  "/value/indices/1": 1
}
```

## HLS Unencrypted Media Playlist Timeline

Service ID: `hls-unencrypted-media-playlist-timeline`. USD 1.00 per job.

Parse a bounded standalone HLS media playlist with EXTINF, media-sequence, target-duration, discontinuity and endlist tags; encryption, maps, byte ranges and master playlists reject. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=hls-unencrypted-media-playlist-timeline) · [Technical reference](https://www.rfc-editor.org/rfc/rfc8216)

Example input:

```json
{
  "data": {
    "text": "#EXTM3U\n#EXT-X-TARGETDURATION:5\n#EXT-X-MEDIA-SEQUENCE:7\n#EXTINF:4.5,one\na.ts\n#EXTINF:5,two\nb.ts\n#EXT-X-ENDLIST\n"
  }
}
```

Selected expected result fields:

```json
{
  "/value/segmentCount": 2,
  "/value/segments/1/sequence": 8
}
```

## MPEG Elementary Start Code Directory

Service ID: `mpeg-elementary-start-code-directory`. USD 1.00 per job.

Index supplied MPEG elementary stream start-code units and payload spans; slice, picture, sequence, GOP, extension and sequence-end codes are recognized without decoding pictures. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=mpeg-elementary-start-code-directory) · [Technical reference](https://mpeg.chiariglione.org/standards/mpeg-1/video.html)

Example input:

```json
{
  "data": {
    "hex": "000001b300000001b7"
  }
}
```

Selected expected result fields:

```json
{
  "/value/unitCount": 2,
  "/value/units/0/code": 179
}
```

## ID3v23 Latin1 Text Frame Decoder

Service ID: `id3v23-latin1-text-frame-decoder`. USD 1.00 per job.

Decode a complete unflagged ID3v2.3 tag containing supported non-user Latin1 text frames and zero padding only. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=id3v23-latin1-text-frame-decoder) · [Technical reference](https://id3.org/id3v2.3.0)

Example input:

```json
{
  "data": {
    "hex": "4944330300000000000d54495432000000030000004142"
  }
}
```

Selected expected result fields:

```json
{
  "/value/frames/0/text": "AB"
}
```

## FLAC Vorbis Comment Payload Decoder

Service ID: `flac-vorbis-comment-payload-decoder`. USD 1.00 per job.

Decode one supplied FLAC VORBIS_COMMENT metadata payload with little-endian lengths, strict UTF8 and ASCII field names; no FLAC audio decoding is claimed. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=flac-vorbis-comment-payload-decoder) · [Technical reference](https://www.rfc-editor.org/rfc/rfc9639.html#section-8.6)

Example input:

```json
{
  "data": {
    "hex": "010000007601000000070000005449544c453d58"
  }
}
```

Selected expected result fields:

```json
{
  "/value/vendor": "v",
  "/value/comments/0/value": "X"
}
```

## Ogg Logical Stream Packet Reassembly

Service ID: `ogg-logical-stream-packet-reassembly`. USD 1.00 per job.

Reassemble exact packet bytes across complete CRC-verified Ogg version-zero pages in one logical stream. Require BOS, EOS, contiguous sequence numbers from zero and coherent continuation flags. No multiplexing, chained streams, codec decoding or granule-time interpretation. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ogg-logical-stream-packet-reassembly) · [Technical reference](https://xiph.org/ogg/doc/framing.html)

Example input:

```json
{
  "data": {
    "hex": "4f676753000200000000000000000700000000000000474f013f01ff4141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414f6767530005000000000000000007000000010000008227dec302010042"
  }
}
```

Selected expected result fields:

```json
{
  "/value/pageCount": 2,
  "/value/packetCount": 2,
  "/value/packets/0/byteLength": 256,
  "/value/packets/0/firstPage": 0,
  "/value/packets/0/lastPage": 1,
  "/value/packets/1/hex": ""
}
```

## RIFF WAVE Cue Point Table Decoder

Service ID: `riff-wave-cue-point-table-decoder`. USD 1.00 per job.

Decode a supplied cue chunk payload for linear PCM data cues, retaining cue IDs, positions and sample offsets; audio bytes and labels are excluded. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=riff-wave-cue-point-table-decoder) · [Technical reference](https://www.mmsp.ece.mcgill.ca/Documents/AudioFormats/WAVE/Docs/riffmci.pdf)

Example input:

```json
{
  "data": {
    "hex": "01000000070000000000000064617461000000000000000078000000"
  }
}
```

Selected expected result fields:

```json
{
  "/value/cues/0/sampleOffset": 120
}
```

## PDF Classic Xref Subsection Decoder

Service ID: `pdf-classic-xref-subsection-decoder`. USD 1.00 per job.

Parse a standalone classic PDF xref table into object-number, byte-offset, generation and in-use entries; trailers, streams and object dereferencing are excluded. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pdf-classic-xref-subsection-decoder) · [Technical reference](https://opensource.adobe.com/dc-acrobat-sdk-docs/pdfstandards/PDF32000_2008.pdf)

Example input:

```json
{
  "data": {
    "text": "xref\n0 2\n0000000000 65535 f \n0000000017 00000 n \n"
  }
}
```

Selected expected result fields:

```json
{
  "/value/entries/1/offset": 17
}
```

## EPS DSC Page Section Index

Service ID: `eps-dsc-page-section-index`. USD 1.00 per job.

Index DSC page markers and declared integer bounding box from an ASCII EPSF document; PostScript content is retained as opaque lines and never executed. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=eps-dsc-page-section-index) · [Technical reference](https://www.adobe.com/content/dam/acom/en/devnet/actionscript/articles/5001.DSC_Spec.pdf)

Example input:

```json
{
  "data": {
    "text": "%!PS-Adobe-3.0 EPSF-3.0\n%%BoundingBox: 0 0 20 10\n%%Pages: 1\n%%EndComments\n%%Page: one 1\nshowpage\n%%EOF\n"
  }
}
```

Selected expected result fields:

```json
{
  "/value/pageCount": 1,
  "/value/boundingBox/2": 20
}
```

## BDF21 Bitmap Font Glyph Decoder

Service ID: `bdf21-bitmap-font-glyph-decoder`. USD 1.00 per job.

Parse a strict BDF2.1 bitmap font with zero property records, integer glyph metrics and bounded hexadecimal bitmap rows. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=bdf21-bitmap-font-glyph-decoder) · [Technical reference](https://www.x.org/docs/BDF/bdf.pdf)

Example input:

```json
{
  "data": {
    "text": "STARTFONT 2.1\nFONT test\nSIZE 8 75 75\nFONTBOUNDINGBOX 8 1 0 0\nSTARTPROPERTIES 0\nENDPROPERTIES\nCHARS 1\nSTARTCHAR A\nENCODING 65\nSWIDTH 500 0\nDWIDTH 8 0\nBBX 8 1 0 0\nBITMAP\n80\nENDCHAR\nENDFONT\n"
  }
}
```

Selected expected result fields:

```json
{
  "/value/glyphs/0/encoding": 65,
  "/value/glyphs/0/bitmap/0": "80"
}
```

## XPM2 Plain Text RGBA Raster

Service ID: `xpm2-plain-text-rgba-raster`. USD 1.00 per job.

Decode plain XPM2 pixmaps with explicit hexadecimal RGB colors or None transparency and bounded fixed-width pixel symbols. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=xpm2-plain-text-rgba-raster) · [Technical reference](https://www.x.org/docs/XPM/xpm.pdf)

Example input:

```json
{
  "data": {
    "text": "! XPM2\n2 1 2 1\na c #ff0000\nb c None\nab\n"
  }
}
```

Selected expected result fields:

```json
{
  "/value/pixels/0/0": 255,
  "/value/pixels/1/3": 0
}
```

## XBM Unsigned Byte Bitmap Decoder

Service ID: `xbm-unsigned-byte-bitmap-decoder`. USD 1.00 per job.

Decode strict X11 unsigned-char XBM source containing one named width, height and hexadecimal byte array; C expressions and code reject. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=xbm-unsigned-byte-bitmap-decoder) · [Technical reference](https://www.x.org/releases/current/doc/libX11/libX11/libX11.html)

Example input:

```json
{
  "data": {
    "text": "#define icon_width 3\n#define icon_height 1\nstatic unsigned char icon_bits[] = { 0x05 };\n"
  }
}
```

Selected expected result fields:

```json
{
  "/value/pixels/0": 1,
  "/value/pixels/1": 0,
  "/value/pixels/2": 1
}
```

## PSF2 Bitmap Font Raster Decoder

Service ID: `psf2-bitmap-font-raster-decoder`. USD 1.00 per job.

Decode complete PSF2 version-zero bitmap fonts without Unicode tables, enforcing exact glyph and row-stride sizes. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=psf2-bitmap-font-raster-decoder) · [Technical reference](https://kernel.googlesource.com/pub/scm/linux/kernel/git/legion/kbd/+/639fd069b23347f1aad19cec3034fa7e325082f7/src/psf.h)

Example input:

```json
{
  "data": {
    "hex": "72b54a860000000020000000000000000100000001000000010000000800000080"
  }
}
```

Selected expected result fields:

```json
{
  "/value/glyphs/0/onPixels": 1
}
```

## JASC PAL RGB Palette Decoder

Service ID: `jasc-pal-rgb-palette-decoder`. USD 1.00 per job.

Parse complete JASC-PAL 0100 text palettes with exact color count and integer RGB channel bounds. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=jasc-pal-rgb-palette-decoder) · [Technical reference](https://github.com/aseprite/aseprite/blob/main/src/doc/file/pal_file.cpp)

Example input:

```json
{
  "data": {
    "text": "JASC-PAL\n0100\n2\n255 0 0\n0 128 255\n"
  }
}
```

Selected expected result fields:

```json
{
  "/value/colors/1/1": 128
}
```

## ASE RGB Swatch Block Decoder

Service ID: `ase-rgb-swatch-block-decoder`. USD 1.00 per job.

Decode complete Adobe Swatch Exchange version-one files containing RGB color-entry blocks with UTF16BE names and finite normalized channels; group and non-RGB blocks reject. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=ase-rgb-swatch-block-decoder) · [Technical reference](https://github.com/behreajj/AsepriteSwatchExchange)

Example input:

```json
{
  "data": {
    "hex": "41534546000100000000000100010000001c00040052006500640000524742203f80000000000000000000000002"
  }
}
```

Selected expected result fields:

```json
{
  "/value/swatches/0/name": "Red",
  "/value/swatches/0/rgb/0": 1
}
```

## Doom WAD Lump Directory Decoder

Service ID: `doom-wad-lump-directory-decoder`. USD 1.00 per job.

Decode a complete IWAD or PWAD lump directory with ASCII names and supplied-data span bounds; game content and map semantics are opaque. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=doom-wad-lump-directory-decoder) · [Technical reference](https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.10/w_wad.c)

Example input:

```json
{
  "data": {
    "hex": "50574144010000000f0000000102030c000000030000005445535400000000"
  }
}
```

Selected expected result fields:

```json
{
  "/value/lumps/0/name": "TEST",
  "/value/lumps/0/size": 3
}
```

## Quake PAK File Directory Decoder

Service ID: `quake-pak-file-directory-decoder`. USD 1.00 per job.

Decode complete Quake PACK archives with fixed path directory entries, contained file spans and safe relative path names; content is not executed. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=quake-pak-file-directory-decoder) · [Technical reference](https://github.com/id-Software/Quake/blob/master/WinQuake/common.c)

Example input:

```json
{
  "data": {
    "hex": "5041434b0e0000004000000001026d6170732f612e627370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c00000002000000"
  }
}
```

Selected expected result fields:

```json
{
  "/value/files/0/path": "maps/a.bsp",
  "/value/files/0/size": 2
}
```

## PCF Bitmap Font Table Directory

Service ID: `pcf-bitmap-font-table-directory`. USD 1.00 per job.

Decode the PCF table directory and validate unique table-type bits, aligned nonoverlapping supplied table spans and format-header agreement. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=pcf-bitmap-font-table-directory) · [Technical reference](https://fontforge.org/docs/techref/pcf-format.html)

Example input:

```json
{
  "data": {
    "hex": "01666370010000000100000000000000040000001800000000000000"
  }
}
```

Selected expected result fields:

```json
{
  "/value/tables/0/type": 1,
  "/value/tableCount": 1
}
```

## Blender Legacy File Block Envelope Directory

Service ID: `blender-file-block-envelope-directory`. USD 1.00 per job.

Decode legacy pre-5 Blender file block envelopes using the declared pointer width and endianness, requiring a terminal ENDB block; SDNA and scene content are not interpreted. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=blender-file-block-envelope-directory) · [Technical reference](https://github.com/blender/blender/blob/blender-v4.5-release/source/blender/blenloader/intern/readfile.cc)

Example input:

```json
{
  "data": {
    "hex": "424c454e4445525f76333030454e444200000000000000000000000000000000"
  }
}
```

Selected expected result fields:

```json
{
  "/value/pointerBytes": 4,
  "/value/blockCount": 0
}
```

## NIfTI1 Array Header Layout Inspection

Service ID: `nifti1-array-header-layout-inspection`. USD 1.00 per job.

Inspect an exact 348-byte NIfTI1 header for supported scalar datatype, dimensions, bit depth, voxel spacing and file-layout fields; no medical interpretation or image data validation is provided. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=nifti1-array-header-layout-inspection) · [Technical reference](https://afni.nimh.nih.gov/pub/dist/doc/nifti/nifti1_h.pdf)

Example input:

```json
{
  "data": {
    "hex": "5c010000000000000000000000000000000000000000000000000000000000000000000000000000020002000300000000000000000000000000000000000000000000000000020008000000000000000000803f0000803f00000000000000000000000000000000000000000000b043000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e2b3100"
  }
}
```

Selected expected result fields:

```json
{
  "/value/elementCount": 6,
  "/value/shape/1": 3
}
```

## NumPy NPY1 Scalar Array Decoder

Service ID: `numpy-npy1-scalar-array-decoder`. USD 1.00 per job.

Decode complete NPY1.0 arrays with a strict literal header and supported nonobject integer or finite floating scalar dtype; arbitrary Python literals and pickle data reject. Bounded deterministic supplied-data profile; no program execution, external-system access or assurance claim. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Open this service](https://gatewayinformationgroup.com/data-tools?tool=numpy-npy1-scalar-array-decoder) · [Technical reference](https://numpy.org/doc/stable/reference/generated/numpy.lib.format.html)

Example input:

```json
{
  "data": {
    "hex": "934e554d5059010046007b276465736372273a20277c7531272c2027666f727472616e5f6f72646572273a2046616c73652c20277368617065273a2028332c292c207d2020202020202020202020200a010203"
  }
}
```

Selected expected result fields:

```json
{
  "/value/values/2": 3,
  "/value/shape/0": 3
}
```

Use authorized, non-sensitive input. Each service applies only its stated profile and does not change external systems or provide professional certification. A quote is unpaid; a signature alone does not establish settlement.