# Operational reports and developer utilities

Each service is a one-time job with a clear processing scope. Review its example, exact price and checkout terms before paying. Private JSON result access lasts 30 days; save a downloaded copy. There is no recurring commitment.

Use authorized non-sensitive input. A prepared quote is unpaid and a signature alone does not establish settlement. Each service validates its input and calculations before checkout. Input and computation profiles describe the work included in one job, not limits on payments or voluntary contributions. No account access, external action, professional certification or outcome guarantee is implied.

## Batch Arrival Service Queue Report

USD 19.00 per job.

Estimate queue exposure when requests arrive in indivisible random-size batches. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Compound Poisson batches, IID exponential individual service, FCFS and infinite room. Normalize a PMF within1e-12 of unit mass; require individual arrival below service capacity with slack>=1e-9. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [cs.newpaltz.edu](https://cs.newpaltz.edu/~lik/publications/Bing-Xiong-CN-2016.pdf). No endorsement is implied.

Example input:

```json
{
  "batchRate": 0.5,
  "serviceRate": 2,
  "batchSizes": [
    1,
    2
  ],
  "probabilities": [
    0.5,
    0.5
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/batchMean": 1.5,
  "/individualArrivalRate": 0.75,
  "/utilization": 0.375,
  "/meanInSystem": 0.8,
  "/meanWaitingTime": 0.5666666666666667
}
```

## General Service Queue Moments Report

USD 19.00 per job.

Separate mean service demand from service-time variability in single-server waiting exposure. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Pollaczek-Khinchine M/G/1 with Poisson arrivals, supplied first two service moments and FCFS; second moment must be at least mean squared; utilization<1 with slack>=1e-9. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/urban_or_book/www/book/chapter4/4.7.html). No endorsement is implied.

Example input:

```json
{
  "arrivalRate": 0.5,
  "serviceMean": 1,
  "serviceSecondMoment": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/utilization": 0.5,
  "/meanWaitingTime": 0.5,
  "/meanInQueue": 0.25,
  "/meanSojournTime": 1.5
}
```

## Variable Arrival Queue Approximation Report

USD 19.00 per job.

Compare arrival and service variability contributions to approximate single-server waiting. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Kingman GI/G/1 moment approximation, IID renewals and independent service. SCVs are squared coefficients of variation; require utilization slack>=1e-9. An approximation, no exact tail probability. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/urban_or_book/www/book/chapter4/4.8.3.html). No endorsement is implied.

Example input:

```json
{
  "arrivalRate": 0.5,
  "serviceMean": 1,
  "arrivalScv": 2,
  "serviceScv": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/utilization": 0.5,
  "/approximateWaitingTime": 1,
  "/approximateQueueLength": 0.5
}
```

## Abandoning Contact Queue Report

USD 19.00 per job.

Reconcile served and abandoning request flows under exponential patience. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Erlang-A M/M/c+M. Rates positive; arrival/service<=100 and arrival/patience<=200. At most2048 birth-death states; require probability-tail bound<=1e-14 and report it. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [aviman.technion.ac.il](https://aviman.technion.ac.il/files/References/Mini_course_generic/4_Generic_Seminar_Printout_9.pdf). No endorsement is implied.

Example input:

```json
{
  "arrivalRate": 1,
  "serviceRate": 1,
  "patienceRate": 1,
  "servers": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/busyProbability": 0.6321205588285577,
  "/meanQueueLength": 0.36787944117144233,
  "/abandonmentFraction": 0.36787944117144233,
  "/servedRate": 0.6321205588285577
}
```

## Finite Buffer Multiserver Queue Report

USD 19.00 per job.

Evaluate rejection, occupancy and admitted-request waiting for a finite waiting room. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. M/M/c/K, capacity includes service and waiting; require K>=c. Finite birth-death log weights remain stable at overloaded rates. Waiting time refers only to admitted arrivals. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/urban_or_book/www/book/chapter4/4.6.4.html). No endorsement is implied.

Example input:

```json
{
  "arrivalRate": 1,
  "serviceRate": 1,
  "servers": 1,
  "capacity": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/blockingProbability": 0.3333333333333333,
  "/effectiveArrivalRate": 0.6666666666666666,
  "/meanInSystem": 1,
  "/meanWaitingTime": 0.5,
  "/stateProbabilities": [
    0.3333333333333333,
    0.3333333333333333,
    0.3333333333333333
  ]
}
```

## Finite Source Repair Queue Report

USD 19.00 per job.

Estimate failed assets and repair waiting when only working assets can generate failures. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Finite-source machine-repair birth rate(N-n)*failureRate; death rate min(n,crews)*repairRate. Require crews<=population. Scenario only, no equipment reliability or maintenance certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/urban_or_book/www/book/chapter4/4.6.5.html). No endorsement is implied.

Example input:

```json
{
  "population": 2,
  "repairCrews": 1,
  "failureRatePerWorking": 1,
  "repairRatePerCrew": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/meanFailed": 1.2,
  "/meanWaiting": 0.4,
  "/meanWorking": 0.8,
  "/repairThroughput": 0.8,
  "/meanRepairSojourn": 1.5,
  "/stateProbabilities": [
    0.2,
    0.4,
    0.4
  ]
}
```

## Priority Service Policy Compare Report

USD 19.00 per job.

Compare preemptive-resume and nonpreemptive mean delays for the same ordered classes. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Lower class index has higher priority, Poisson arrivals, first two service moments and preemptive-resume without loss. Require valid moments and total utilization slack>=1e-9. Preemptive sojourn includes interruptions. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/urban_or_book/www/book/chapter4/4.9.1.html). No endorsement is implied.

Example input:

```json
{
  "classes": [
    {
      "arrivalRate": 0.2,
      "serviceMean": 1,
      "serviceSecondMoment": 2
    },
    {
      "arrivalRate": 0.2,
      "serviceMean": 1,
      "serviceSecondMoment": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/utilization": 0.4,
  "/nonpreemptiveWaiting": [
    0.5,
    0.8333333333333334
  ],
  "/preemptiveSojourn": [
    1.25,
    2.0833333333333335
  ]
}
```

## Open Service Network Balance Report

USD 19.00 per job.

Reconcile routed internal arrival loads and mean work across an open network of single-server stations. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Open Jackson M/M/1 stations. Routing rows sum<=1; every station must reach an exit. Solve lambda=e+P^Tlambda, require each utilization slack>=1e-9. Zero external total gives null network time. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/urban_or_book/www/book/chapter4/4.10.html). No endorsement is implied.

Example input:

```json
{
  "externalRates": [
    0.5,
    0
  ],
  "serviceRates": [
    1,
    1
  ],
  "routing": [
    [
      0,
      0.5
    ],
    [
      0,
      0
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/arrivalRates": [
    0.5,
    0.25
  ],
  "/utilizations": [
    0.5,
    0.25
  ],
  "/meanStationOccupancies": [
    1,
    0.3333333333333333
  ],
  "/meanNetworkSojourn": 2.6666666666666665
}
```

## Vacation Service Queue Report

USD 19.00 per job.

Measure the waiting contribution of an unavailable server under repeated exhaustive vacations. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. M/G/1 exhaustive multiple-vacation decomposition. Every empty system triggers IID vacations until work is present; second moments>=mean² and utilization slack>=1e-9. Distinct from single-vacation policy. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/modiano/www/6.263/lec8.pdf). No endorsement is implied.

Example input:

```json
{
  "arrivalRate": 0.5,
  "serviceMean": 1,
  "serviceSecondMoment": 2,
  "vacationMean": 2,
  "vacationSecondMoment": 4
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/utilization": 0.5,
  "/serviceWaitingContribution": 1,
  "/vacationWaitingContribution": 1,
  "/meanWaitingTime": 2
}
```

## Infinite Server Transient Load Report

USD 19.00 per job.

Trace startup occupancy and idle probability when parallel service capacity is unrestricted. Stationary supplied-data queue model with consistent time units; no staffing, service-level or live-system guarantee. Transient M/M/infinity with deterministic initial occupancy, Poisson immigration and exponential departure. Occupancy=initial Binomial survivors+Poisson new survivors. No blocking, abandonment or real capacity sizing. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/modiano/www/6.263/lec5-6.pdf). No endorsement is implied.

Example input:

```json
{
  "arrivalRate": 2,
  "serviceRate": 1,
  "initialUnits": 0,
  "times": [
    0,
    0.6931471805599453
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/meanOccupancies": [
    0,
    1
  ],
  "/variances": [
    0,
    1
  ],
  "/emptyProbabilities": [
    1,
    0.36787944117144233
  ],
  "/stationaryMean": 2
}
```

## Straight Fin Heat Transfer Report

USD 19.00 per job.

Compare straight-fin efficiency, tip temperature and ideal heat removal from caller-supplied geometry. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Uniform 1D fin with adiabatic tip, no contact resistance, m=sqrt(hP/kA); transverseBiot=hA/kP is reported without certifying 1D applicability. h=0 has efficiency1 and zero heat. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/16.unified/OldFiles/www/SPRING/thermodynamics/notes/node128.html). No endorsement is implied.

Example input:

```json
{
  "hWm2K": 1,
  "perimeterM": 1,
  "conductivityWmK": 100,
  "crossSectionM2": 0.01,
  "lengthM": 1,
  "baseC": 100,
  "ambientC": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/efficiency": 0.7615941559557649,
  "/heatWatts": 76.15941559557649,
  "/tipC": 64.80542736638854,
  "/transverseBiot": 0.0001
}
```

## Radial Insulation Heat Flow Report

USD 19.00 per job.

Reconcile radial layer resistances and interface temperatures around a cylindrical asset. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Steady concentric cylindrical layers, positive strictly increasing radii. Resistance ln(ro/ri)/(2*pi*k*L), no axial loss, convection or contact resistance. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/course/16/16.unified/www/FALL/thermodynamics/notes/node119.html). No endorsement is implied.

Example input:

```json
{
  "innerRadiusM": 0.1,
  "lengthM": 1,
  "layers": [
    {
      "outerRadiusM": 0.2,
      "conductivityWmK": 1
    }
  ],
  "innerC": 100,
  "outerC": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/layerResistancesKW": [
    0.1103178000763258
  ],
  "/totalResistanceKW": 0.1103178000763258,
  "/heatWatts": 906.4720283654387,
  "/interfaceTemperaturesC": [
    100,
    0
  ]
}
```

## Lumped Body Cooling Trace Report

USD 19.00 per job.

Trace a small body temperature and removed energy under constant convection. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Lumped capacitance requires supplied h*(V/A)/k<=.1. Uniform initial temperature, constant ambient and convection; no phase change/radiation. Negative removed energy means warming. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/3-185-transport-phenomena-in-materials-engineering-fall-2003/ee73a0b0777ffa761e40337e841bbdad_ps4sol.pdf). No endorsement is implied.

Example input:

```json
{
  "massKg": 1,
  "heatCapacityJkgK": 1000,
  "hWm2K": 10,
  "surfaceM2": 1,
  "volumeM3": 0.001,
  "conductivityWmK": 100,
  "initialC": 100,
  "ambientC": 0,
  "timesS": [
    0,
    69.31471805599453
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/biot": 0.0001,
  "/timeConstantS": 100,
  "/temperaturesC": [
    100,
    50
  ],
  "/removedEnergyJ": [
    0,
    50000
  ]
}
```

## Counterflow NTU Duty Report

USD 19.00 per job.

Estimate counterflow duty and both outlet temperatures from inlet conditions and heat capacities. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Ideal counterflow epsilon-NTU, no heat loss or phase change. Require hotIn>=coldIn. Balanced-capacity limit is NTU/(1+NTU); stable expm1 formulation otherwise. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/10.302/www/Fall2001/EXAMS/exam3_solutions.pdf). No endorsement is implied.

Example input:

```json
{
  "uaWK": 100,
  "hotCapacityWK": 100,
  "coldCapacityWK": 100,
  "hotInC": 100,
  "coldInC": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/ntu": 1,
  "/capacityRatio": 1,
  "/effectiveness": 0.5,
  "/heatWatts": 5000,
  "/hotOutC": 50,
  "/coldOutC": 50
}
```

## Gray Surface Radiation Exchange Report

USD 19.00 per job.

Reconcile diffuse gray two-surface radiation resistance and net heat direction. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Two-surface diffuse gray enclosure exchange; reciprocity A1*F12=A2*F21 must give F21<=1. sigma=5.670374419e-8 W/m²/K⁴. User supplies geometry/view factor; no surrounding third surface. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [tfaws.nasa.gov](https://tfaws.nasa.gov/TFAWS00/CP-2002-211486.pdf). No endorsement is implied.

Example input:

```json
{
  "area1M2": 1,
  "area2M2": 1,
  "emissivity1": 0.5,
  "emissivity2": 0.5,
  "viewFactor12": 1,
  "temperature1K": 400,
  "temperature2K": 300
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/reciprocalViewFactor21": 1,
  "/radiationResistancePerM2": 3,
  "/netHeatWatts": 330.7718411083333
}
```

## Moist Air Stream Mixing Report

USD 19.00 per job.

Reconcile dry-air flow, humidity and enthalpy when supplied moist streams mix adiabatically. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Dry-air mass basis: mix h=1.006T+W(2501+1.86T), mix W by dry-air flow and recover T. Same pressure, no water addition, condensation or saturation calculation; supplied streams must satisfy those assumptions. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/4-42j-fundamentals-of-energy-in-buildings-fall-2010/a860d453697831aca223049667c430bb_MIT4_42JF10_water_vapor.pdf). No endorsement is implied.

Example input:

```json
{
  "streams": [
    {
      "dryAirKgS": 1,
      "temperatureC": 20,
      "humidityKgKg": 0
    },
    {
      "dryAirKgS": 1,
      "temperatureC": 20,
      "humidityKgKg": 0.02
    }
  ],
  "pressurePa": 100000
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/dryAirKgS": 2,
  "/humidityKgKg": 0.01,
  "/enthalpyKjKg": 45.502,
  "/temperatureC": 20,
  "/vaporPressurePa": 1582.3285547010983
}
```

## Adiabatic Compressor State Report

USD 19.00 per job.

Compare ideal and efficiency-adjusted compressor temperature, work and shaft demand. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Calorically perfect gas with constant gamma/cp; ideal temperature ratio=r^((gamma-1)/gamma), actual rise=ideal rise/efficiency. No cooling, kinetic-energy change or map/surge assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.grc.nasa.gov](https://www.grc.nasa.gov/www/k-12/airplane/compth.html). No endorsement is implied.

Example input:

```json
{
  "inletK": 300,
  "pressureRatio": 8,
  "heatCapacityRatio": 1.5,
  "isentropicEfficiency": 0.75,
  "cpJkgK": 1000,
  "massKgS": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/idealOutletK": 600,
  "/outletK": 700,
  "/specificWorkJkg": 400000,
  "/shaftWatts": 400000
}
```

## Phase Change Store Enthalpy Report

USD 19.00 per job.

Map accumulated thermal energy into sensible temperature and melt fraction for a pure storage material. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. Reference is a fully solid state strictly below melting. Piecewise constant solid/liquid heat capacity and isothermal latent interval, no supercooling, boiling, hysteresis or loss. Reject computed temperatures at/below absolute zero. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/dbm/archive/%21JYLAIMS.htm). No endorsement is implied.

Example input:

```json
{
  "massKg": 2,
  "solidCpKjKgK": 2,
  "liquidCpKjKgK": 4,
  "meltingC": 0,
  "referenceC": -10,
  "latentKjKg": 100,
  "heatAddedKj": [
    0,
    40,
    140,
    240,
    320
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/temperaturesC": [
    -10,
    0,
    0,
    0,
    10
  ],
  "/liquidFractions": [
    0,
    0,
    0.5,
    1,
    1
  ],
  "/specificEnthalpiesKjKg": [
    0,
    20,
    70,
    120,
    160
  ]
}
```

## Hydrocarbon Stoichiometric Air Report

USD 19.00 per job.

Balance ideal complete-combustion oxygen, dry air and exhaust mole quantities for a supplied fuel formula. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. One mole CxHyOz, oxygen requirement x+y/4-z/2>0, excess-air ratio>=1. Balance air as O2/inert N2, nominal atomic masses12/1/16 and molar masses32/28. No kinetics, temperature, pollutants or emissions compliance. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node107.html). No endorsement is implied.

Example input:

```json
{
  "carbonAtoms": 1,
  "hydrogenAtoms": 4,
  "oxygenAtoms": 0,
  "airOxygenMoleFraction": 0.2,
  "excessAirRatio": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/stoichiometricOxygenMoles": 2,
  "/airMoles": 10,
  "/co2Moles": 1,
  "/waterMoles": 2,
  "/excessOxygenMoles": 0,
  "/inertNitrogenMoles": 8,
  "/airFuelMassRatio": 18
}
```

## Enthalpy Cycle Energy Balance Report

USD 19.00 per job.

Reconcile pump, heater, turbine and condenser specific energies for supplied cycle states. Supplied-data thermal scenario with declared SI units and constant properties; no safety, equipment selection or professional certification. States1 pump-in,2 pump-out,3 turbine-in,4 turbine-out. Positive heat input/net work, nonnegative pump work/heat rejection. Enthalpies supplied consistently; no steam-property lookup or thermodynamic-state certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/16.unified/OldFiles/www/FALL/thermodynamics/notes/node65.html). No endorsement is implied.

Example input:

```json
{
  "enthalpiesKjKg": [
    100,
    110,
    1000,
    400
  ],
  "massKgS": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/pumpWorkKjKg": 10,
  "/turbineWorkKjKg": 600,
  "/netWorkKjKg": 590,
  "/heatInKjKg": 890,
  "/heatOutKjKg": 300,
  "/efficiency": 0.6629213483146067,
  "/netPowerKw": 1180
}
```

## Manning Open Channel Flow Report

USD 19.00 per job.

Reconcile uniform trapezoidal channel flow, hydraulic radius and Froude number. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Uniform open-channel Manning formula in SI with coefficient1; sideSlope is horizontal/vertical on both sides, hydraulic depth=A/topWidth. Bed slope0 gives zero flow; no backwater or roughness inference. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.usbr.gov](https://www.usbr.gov/tsc/techreferences/hydraulics_lab/pubs/manuals/GravityDams.pdf). No endorsement is implied.

Example input:

```json
{
  "bottomWidthM": 2,
  "depthM": 1,
  "sideSlope": 0,
  "roughnessN": 0.1,
  "bedSlope": 0.01,
  "gravityMs2": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/areaM2": 2,
  "/wettedPerimeterM": 4,
  "/hydraulicRadiusM": 0.5,
  "/flowM3S": 1.2599210498948732,
  "/velocityMS": 0.6299605249474366,
  "/froude": 0.6299605249474366
}
```

## Orifice Discharge Scenario Report

USD 19.00 per job.

Translate a supplied orifice area, differential head and discharge coefficient into volume and mass flow. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Incompressible small-orifice equation Q=Cd*A*sqrt(2*g*head), supplied differential piezometric head, mean exit velocity Q/A. No coefficient calibration, submergence correction or cavitation model. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.usbr.gov](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap09_01.html). No endorsement is implied.

Example input:

```json
{
  "areaM2": 0.01,
  "headM": 2,
  "dischargeCoefficient": 0.6,
  "gravityMs2": 10,
  "densityKgM3": 1000
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/flowM3S": 0.03794733192202056,
  "/meanExitVelocityMS": 3.794733192202055,
  "/massKgS": 37.94733192202055
}
```

## Venturi Flow Inference Report

USD 19.00 per job.

Infer incompressible flow from a supplied main/throat diameter pair and pressure differential. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Horizontal same-density Venturi relation with supplied Cd and pressure taps; require throat<main. No compressibility, Reynolds/coefficient calibration or instrument certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.usbr.gov](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap02_14.html). No endorsement is implied.

Example input:

```json
{
  "mainDiameterM": 0.2,
  "throatDiameterM": 0.1,
  "differentialPa": 1000,
  "densityKgM3": 1000,
  "dischargeCoefficient": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/diameterRatio": 0.5,
  "/flowM3S": 0.011471474419090952,
  "/mainVelocityMS": 0.3651483716701107,
  "/throatVelocityMS": 1.4605934866804429
}
```

## Compressible Nozzle Regime Report

USD 19.00 per job.

Resolve ideal converging-nozzle choking, exit state and mass flow from stagnation conditions. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Calorically perfect ideal gas, isentropic converging nozzle. Exit Mach caps at1; back pressure<=critical gives throat pressure, not downstream jet pressure. Cd scales mass flow only. No shocks/diverging section or real-gas correction. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.grc.nasa.gov](https://www.grc.nasa.gov/www/k-12/airplane/mflchk.html). No endorsement is implied.

Example input:

```json
{
  "stagnationPa": 100000,
  "backPressurePa": 0,
  "stagnationK": 300,
  "heatCapacityRatio": 1.4,
  "gasConstantJkgK": 287,
  "areaM2": 0.01,
  "dischargeCoefficient": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/choked": true,
  "/criticalPressureRatio": 0.5282817877171742,
  "/mach": 1,
  "/exitPa": 52828.178771717416,
  "/exitK": 250,
  "/velocityMS": 316.9384798348096,
  "/massKgS": 2.333558560606227
}
```

## Rectangular Channel Hydraulic Jump Report

USD 19.00 per job.

Reconcile conjugate depths and ideal dissipated head for a supplied supercritical rectangular flow. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Horizontal prismatic rectangular channel, hydrostatic end sections and negligible boundary shear. Require upstream Froude>1. Conjugate-depth momentum model, no jump location, aeration or basin design. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.publications.usace.army.mil](https://www.publications.usace.army.mil/portals/76/publications/engineermanuals/em_1110-2-1601.pdf). No endorsement is implied.

Example input:

```json
{
  "upstreamDepthM": 1,
  "upstreamVelocityMS": 9.486832980505138,
  "widthM": 2,
  "gravityMs2": 10
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/upstreamFroude": 3,
  "/downstreamDepthM": 3.772001872658765,
  "/downstreamVelocityMS": 2.5150658193650814,
  "/flowM3S": 18.973665961010276,
  "/headLossM": 1.4117203235543068
}
```

## Joukowsky Pressure Transient Report

USD 19.00 per job.

Screen a declared velocity change against an ideal instantaneous pressure step and closure time scale. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Signed Joukowsky step rho*c*(vBefore-vAfter) and round-trip2L/c; rapidClosure means supplied closureTime<=2L/c. Instantaneous ideal model is still returned for slow closure with flagfalse. No full transient, reflection, cavitation or allowable pressure assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ntrs.nasa.gov](https://ntrs.nasa.gov/api/citations/20210022275/downloads/20210022275.pdf). No endorsement is implied.

Example input:

```json
{
  "densityKgM3": 1000,
  "waveSpeedMS": 1000,
  "velocityBeforeMS": 2,
  "velocityAfterMS": 0,
  "pipeLengthM": 1000,
  "closureTimeS": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/pressureStepPa": 2000000,
  "/roundTripTimeS": 2,
  "/rapidClosure": true
}
```

## Ergun Packed Bed Pressure Report

USD 19.00 per job.

Separate viscous and inertial pressure-gradient contributions in a supplied packed-bed scenario. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Ergun150/1.75 correlation for a uniform fixed bed of equivalent spheres, superficial velocity and constant incompressible properties. Particle Re=rho*v*d/mu, not modified bed Re; no fluidization, wall or shape correction. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [fluids.readthedocs.io](https://fluids.readthedocs.io/fluids.packed_bed.html). No endorsement is implied.

Example input:

```json
{
  "voidFraction": 0.5,
  "particleDiameterM": 0.01,
  "lengthM": 1,
  "viscosityPas": 0.001,
  "densityKgM3": 1,
  "superficialVelocityMS": 0.1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/viscousGradientPaM": 300,
  "/inertialGradientPaM": 7,
  "/pressureDropPa": 307,
  "/particleReynolds": 1
}
```

## Parallel Pipe Head Distribution Report

USD 19.00 per job.

Balance a total flow among parallel branches with supplied quadratic head resistances. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Common inlet/outlet heads and branch law h=R*Q² with R in m/(m³/s)². Positive fixed resistances, forward flows, no static head difference/pump curve or iterative friction-factor calculation; power=rho*g*Q*h. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.usbr.gov](https://www.usbr.gov/tsc/techreferences/mands/wmm/chap02_14.html). No endorsement is implied.

Example input:

```json
{
  "totalFlowM3S": 3,
  "resistances": [
    1,
    4
  ],
  "densityKgM3": 1000,
  "gravityMs2": 10
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/commonHeadM": 4,
  "/branchFlowsM3S": [
    2,
    1
  ],
  "/hydraulicWatts": 120000
}
```

## Capillary Rise Scenario Report

USD 19.00 per job.

Resolve equilibrium rise or depression, meniscus pressure and capillary length from supplied wetting properties. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Circular narrow tube, static Jurin/Laplace balance with supplied equilibrium contact angle. Positive pressure denotes liquid suction/rise; angle>90 gives depression. No contact-angle hysteresis, dynamic wetting or confinement correction. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/nnf/education/wettability/gravity.html). No endorsement is implied.

Example input:

```json
{
  "surfaceTensionNm": 0.05,
  "contactAngleDeg": 0,
  "densityKgM3": 1000,
  "gravityMs2": 10,
  "tubeRadiusM": 0.001
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/heightM": 0.01,
  "/meniscusPressurePa": 100,
  "/capillaryLengthM": 0.00223606797749979
}
```

## Sieve Gradation Characteristics Report

USD 19.00 per job.

Reconcile supplied retained masses into passing fractions and interpolated gradation descriptors. Supplied-data SI fluid scenario; constant properties and declared idealizations, no equipment selection, safety or professional certification. Strictly decreasing sieve openings ending with0 pan and positive total mass. Log-diameter/linear-passing interpolation between measured positive openings only; exact plateau takes largest matching opening. Unbracketed D-values and dependent ratios returnnull; no soil classification or sampling certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.fhwa.dot.gov](https://www.fhwa.dot.gov/engineering/geotech/pubs/nhi06088.pdf). No endorsement is implied.

Example input:

```json
{
  "sieves": [
    {
      "openingMm": 4,
      "retainedMass": 0
    },
    {
      "openingMm": 2,
      "retainedMass": 40
    },
    {
      "openingMm": 1,
      "retainedMass": 30
    },
    {
      "openingMm": 0.5,
      "retainedMass": 20
    },
    {
      "openingMm": 0,
      "retainedMass": 10
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/totalMass": 100,
  "/passingFractions": [
    1,
    0.6,
    0.3,
    0.1,
    0
  ],
  "/d10Mm": 0.5,
  "/d30Mm": 1,
  "/d60Mm": 2,
  "/uniformityCoefficient": 4,
  "/curvatureCoefficient": 1
}
```

## Axial Bar Compatibility Report

USD 19.00 per job.

Reconcile common axial force and segment extensions under an imposed end displacement and thermal changes. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Series collinear linear-elastic segments, no intermediate axial load, fixed uniform properties per segment. Total extension=sum(F*L/EA+alpha*deltaT*L); tension/extension positive. End displacement is imposed; no buckling, yield or joint slip assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.tudelft.nl](https://ocw.tudelft.nl/course-readings/axial-loaded-members-summary-key-formulas-2/). No endorsement is implied.

Example input:

```json
{
  "segments": [
    {
      "lengthM": 1,
      "areaM2": 1,
      "youngPa": 1000,
      "expansionPerK": 0.001,
      "temperatureChangeK": 10
    },
    {
      "lengthM": 1,
      "areaM2": 1,
      "youngPa": 1000,
      "expansionPerK": 0,
      "temperatureChangeK": 0
    }
  ],
  "endDisplacementM": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/forceN": -5,
  "/stressesPa": [
    -5,
    -5
  ],
  "/segmentExtensionsM": [
    0.005,
    -0.005
  ],
  "/freeThermalExtensionM": 0.01,
  "/complianceMPerN": 0.002
}
```

## Beam Span Load Deflection Report

USD 19.00 per job.

Reconcile simple-span reactions, moments and elastic deflection from uniform plus central point loading. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Prismatic Euler-Bernoulli small-deflection beam, simple supports at0 and L, constant EI; superpose downward full-span uniform load and central point load. Downward deflection positive; no shear deflection, stress limit or geometric-nonlinearity check. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/13534abb67b86d2fb8ee11a1f4f2b8c4_MIT3_11F99_bdisp.pdf). No endorsement is implied.

Example input:

```json
{
  "lengthM": 2,
  "youngPa": 1000,
  "secondMomentM4": 1,
  "uniformNm": 3,
  "centerLoadN": 4,
  "positionsM": [
    0,
    1,
    2
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/supportReactionN": 5,
  "/maximumMomentNm": 3.5,
  "/midspanDeflectionM": 0.0012916666666666667,
  "/deflectionsM": [
    0,
    0.0012916666666666667,
    0
  ],
  "/momentsNm": [
    0,
    3.5,
    0
  ]
}
```

## Column Buckling Scenario Report

USD 19.00 per job.

Calculate ideal Euler load, effective slenderness and a supplied load ratio. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Straight perfect prismatic elastic column, supplied effective-length factor and weakest-axis I. Euler load=pi²EI/(KL)²; ratio is a hypothetical comparison, not pass/fail. No imperfections, inelasticity, eccentricity or design-code assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.ocw.mit.edu](https://www.ocw.mit.edu/courses/2-002-mechanics-and-materials-ii-spring-2004/bc25a56b5a91ad29ca5c7419616686f7_lec2.pdf). No endorsement is implied.

Example input:

```json
{
  "lengthM": 2,
  "effectiveLengthFactor": 1,
  "youngPa": 1000,
  "secondMomentM4": 0.01,
  "areaM2": 1,
  "appliedCompressionN": 10
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/effectiveLengthM": 2,
  "/radiusGyrationM": 0.1,
  "/slenderness": 20,
  "/eulerLoadN": 24.674011002723397,
  "/appliedToEulerRatio": 0.4052847345693511
}
```

## Stepped Shaft Torsion Report

USD 19.00 per job.

Reconcile signed twist and surface shear in a series shaft with supplied segment torques. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Circular annular/solid linear-elastic segments, J=pi*(Do⁴-Di⁴)/32 and Do>Di. Caller supplies internal torque in each segment; sum TL/GJ. No torque-load inference, warping, keyway stress or yield assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.tudelft.nl](https://ocw.tudelft.nl/course-readings/summary-key-formulas-torsion-2/). No endorsement is implied.

Example input:

```json
{
  "segments": [
    {
      "lengthM": 1,
      "outerDiameterM": 2,
      "innerDiameterM": 0,
      "shearPa": 1000,
      "torqueNm": 10
    },
    {
      "lengthM": 1,
      "outerDiameterM": 2,
      "innerDiameterM": 0,
      "shearPa": 1000,
      "torqueNm": -10
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/polarMomentsM4": [
    1.5707963267948966,
    1.5707963267948966
  ],
  "/segmentTwistsRad": [
    0.006366197723675814,
    -0.006366197723675814
  ],
  "/outerShearsPa": [
    6.366197723675814,
    -6.366197723675814
  ],
  "/totalTwistRad": 0
}
```

## Flywheel Energy Window Report

USD 19.00 per job.

Trace supplied energy exchanges into flywheel speed and compare them with a declared speed window. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Rigid constant inertia, kinetic energy I*omega²/2. Signed energy changes include caller-accounted losses; reject negative cumulative energy. Speed0 allowed, no reversal. Window comparisons are scenarios, no rotor stress or containment assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/2128c0f4c916bbdc171414c1ef9a17b0_0QF_uCgZW4Y.pdf). No endorsement is implied.

Example input:

```json
{
  "inertiaKgM2": 2,
  "minimumRpm": 0,
  "maximumRpm": 120,
  "initialRpm": 60,
  "energyChangesJ": [
    -29.608813203268074
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/usableWindowJ": 157.91367041742973,
  "/speedsRpm": [
    60,
    30
  ],
  "/energiesJ": [
    39.47841760435743,
    9.869604401089358
  ],
  "/withinWindow": [
    true,
    true
  ],
  "/finalEnergyAboveMinimumJ": 9.869604401089358
}
```

## Harmonic Oscillator Response Report

USD 19.00 per job.

Compare steady harmonic amplitude and lag across supplied driving frequencies for one mass-spring-damper. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Linear SDOF m*xdd+c*xd+k*x=F*cos(omega*t), steady state only. Amplitude F/hypot(k-m*omega²,c*omega), lag atan2(c*omega,k-m*omega²). Undamped exact resonance rejected; no transient, nonlinear or multiple-mode response. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/2-003sc-engineering-dynamics-fall-2011/pages/mechanical-vibration/). No endorsement is implied.

Example input:

```json
{
  "massKg": 1,
  "stiffnessNm": 4,
  "dampingNsM": 2,
  "forceAmplitudeN": 2,
  "angularFrequencies": [
    0,
    2
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/naturalAngularFrequency": 2,
  "/dampingRatio": 0.5,
  "/amplitudesM": [
    0.5,
    0.5
  ],
  "/phaseLagsRad": [
    0,
    1.5707963267948966
  ]
}
```

## Damped Free Response Trace Report

USD 19.00 per job.

Trace displacement and velocity after supplied initial conditions through under, critical or overdamping. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Homogeneous linear SDOF with constant m,c,k and no forcing. All damping regimes, exact equality defines critical; stable near-critical formulas. Oscillatory phase omegaD*time limited to1e7 radians. No forcing/nonlinear or multi-mode response. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/res-8-009-introduction-to-oscillations-and-waves-summer-2017/mitres_8_009su17_lec4.pdf). No endorsement is implied.

Example input:

```json
{
  "massKg": 1,
  "stiffnessNm": 1,
  "dampingNsM": 2,
  "initialDisplacementM": 1,
  "initialVelocityMS": 0,
  "timesS": [
    0,
    1
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/naturalAngularFrequency": 1,
  "/dampingRatio": 1,
  "/regime": "critical",
  "/displacementsM": [
    1,
    0.7357588823428847
  ],
  "/velocitiesMS": [
    0,
    -0.36787944117144233
  ]
}
```

## Hertz Line Contact Scenario Report

USD 19.00 per job.

Reconcile effective curvature/modulus and ideal contact width and peak pressure for parallel cylinders. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Frictionless Hertz line contact between external convex parallel cylinders, load per length=F/L, half-width sqrt(4FR*/piLE*). Elastic half-space/small-contact assumption is caller responsibility; no adhesion, plasticity, edge or fatigue assessment. Zero load returns zero width/pressure. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [e6.ijs.si](https://e6.ijs.si/medusa/wiki/index.php/Hertzian_contact). No endorsement is implied.

Example input:

```json
{
  "loadN": 3.141592653589793,
  "contactLengthM": 1,
  "radius1M": 2,
  "radius2M": 2,
  "young1Pa": 2000,
  "young2Pa": 2000,
  "poisson1": 0,
  "poisson2": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/effectiveRadiusM": 1,
  "/effectiveModulusPa": 1000,
  "/halfWidthM": 0.06324555320336758,
  "/peakPressurePa": 31.622776601683793
}
```

## Capstan Belt Traction Report

USD 19.00 per job.

Reconcile limiting belt tension amplification and torque for supplied friction and wrap. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Flexible belt on circular drum at impending slip, tight/slack=exp(mu*wrap). No centrifugal tension, bending stiffness, wear or strength limit; torque difference times radius. Maximum exponent180 bounds floating output. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/2-141-modeling-and-simulation-of-dynamic-systems-fall-2006/09bbd00ad1a816a401f166e35fbaf231_capstan_amplifie.pdf). No endorsement is implied.

Example input:

```json
{
  "slackTensionN": 100,
  "frictionCoefficient": 0.5,
  "wrapRadians": 1.3862943611198906,
  "drumRadiusM": 0.2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/limitingTensionRatio": 2,
  "/limitingTightTensionN": 200,
  "/tensionDifferenceN": 100,
  "/limitingTorqueNm": 20
}
```

## Rotating Unbalance Resultant Report

USD 19.00 per job.

Reconcile same-speed coplanar unbalance vectors into an excitation force phasor. Supplied-data SI mechanical scenario under declared ideal models; no safety, equipment selection, allowable-load or professional certification. Coplanar point unbalances rotate at one common speed; vector sum m*r then force=omega²*unbalance. Phase normalized[0,360), null when amplitude<=1e-12*sum magnitudes. No couple unbalance, bearing reactions, rotor response or balancing certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/2-003sc-engineering-dynamics-fall-2011/pages/angular-momentum-and-rotating-masses/). No endorsement is implied.

Example input:

```json
{
  "rpm": 60,
  "masses": [
    {
      "massKg": 1,
      "eccentricityM": 1,
      "phaseDeg": 0
    },
    {
      "massKg": 1,
      "eccentricityM": 1,
      "phaseDeg": 90
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/unbalanceXKgM": 1,
  "/unbalanceYKgM": 1,
  "/resultantUnbalanceKgM": 1.4142135623730951,
  "/forceAmplitudeN": 55.830913597111035,
  "/forceXAmplitudeN": 39.47841760435743,
  "/forceYAmplitudeN": 39.47841760435743,
  "/phaseDeg": 45
}
```

## Principal Component Observation Map Report

USD 19.00 per job.

Map centered multivariate observations into principal components with variance accounting and reconstruction error. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Unscaled centered sample covariance divisor n-1; rectangular n2..64,p1..8 and components<=p. Positive total variance. Descending eigenvalues; eigenvector largest absolute loading positive (first index on relative1e-12 loading ties), tied eigenvalues may have nonunique bases. No missing values, standardization or whitening. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.stat.ethz.ch](https://www.stat.ethz.ch/R-manual/R-devel/library/stats/html/prcomp.html). No endorsement is implied.

Example input:

```json
{
  "observations": [
    [
      -1,
      0
    ],
    [
      0,
      0
    ],
    [
      1,
      0
    ]
  ],
  "components": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/means": [
    0,
    0
  ],
  "/eigenvalues": [
    1,
    0
  ],
  "/explainedFractions": [
    1,
    0
  ],
  "/loadings": [
    [
      1,
      0
    ]
  ],
  "/scores": [
    [
      -1
    ],
    [
      0
    ],
    [
      1
    ]
  ],
  "/reconstructionSquaredError": 0
}
```

## Classical Distance Embedding Report

USD 19.00 per job.

Create a classical Euclidean distance embedding and reconcile reconstructed pair distances. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Double-center squared distance matrix and retain requested leading nonnegative axes. Square symmetric exact-zero diagonal, dimensions<n; reject materially negative Gram eigenvalues below -1e-10*largest magnitude. Tiny negative eigenvalues clamp0. Residual sums squared differences of input/reconstructed distances over unordered pairs. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [stat.ethz.ch](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/cmdscale.html). No endorsement is implied.

Example input:

```json
{
  "distances": [
    [
      0,
      2
    ],
    [
      2,
      0
    ]
  ],
  "dimensions": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/eigenvalues": [
    2,
    0
  ],
  "/coordinates": [
    [
      1
    ],
    [
      -1
    ]
  ],
  "/squaredDistanceResidual": 0
}
```

## Contingency Correspondence Map Report

USD 19.00 per job.

Map contingency-table row and column profiles through correspondence principal coordinates. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Nonnegative integer table with positive row/column margins. S=(P-r*c)/sqrt(r*c), eigen S*S-transpose; dimensions<=min(rows-1,cols-1), leading principal coordinates U*sigma/sqrt(r), V*sigma/sqrt(c). Axes with inertia<=1e-24 returnzero. Unsmoothed descriptive associations only. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.stat.ethz.ch](https://www.stat.ethz.ch/R-manual/R-patched/library/MASS/html/corresp.html). No endorsement is implied.

Example input:

```json
{
  "counts": [
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ],
  "dimensions": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/totalCount": 2,
  "/rowMasses": [
    0.5,
    0.5
  ],
  "/columnMasses": [
    0.5,
    0.5
  ],
  "/principalInertias": [
    1
  ],
  "/totalInertia": 1,
  "/rowCoordinates": [
    [
      1
    ],
    [
      -1
    ]
  ],
  "/columnCoordinates": [
    [
      1
    ],
    [
      -1
    ]
  ]
}
```

## Discriminant Model Comparison Report

USD 19.00 per job.

Compare supplied-data LDA and QDA classifications and Gaussian log scores on the same query records. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. 2..8 classes, p<=6, each class n>p, rectangular data. Empirical class priors; QDA unbiased within-class covariance, LDA pooled covariance divisor n-classes. Positive definite covariance minimum eigenvalue>1e-10 maximum. Scores omit shared -p*log(2*pi)/2 and are not normalized posteriors. Lexical class tie rule; no training/test performance claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [scikit-learn.org](https://scikit-learn.org/stable/modules/lda_qda.html). No endorsement is implied.

Example input:

```json
{
  "training": [
    {
      "label": "A",
      "values": [
        -1
      ]
    },
    {
      "label": "A",
      "values": [
        1
      ]
    },
    {
      "label": "B",
      "values": [
        3
      ]
    },
    {
      "label": "B",
      "values": [
        5
      ]
    }
  ],
  "queries": [
    [
      0
    ],
    [
      2
    ],
    [
      4
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/classes": [
    "A",
    "B"
  ],
  "/empiricalPriors": [
    0.5,
    0.5
  ],
  "/classMeans": [
    [
      0
    ],
    [
      4
    ]
  ],
  "/ldaPredictions": [
    "A",
    "A",
    "B"
  ],
  "/qdaPredictions": [
    "A",
    "A",
    "B"
  ],
  "/ldaLogScores": [
    [
      -1.0397207708399179,
      -5.039720770839918
    ],
    [
      -2.039720770839918,
      -2.039720770839918
    ],
    [
      -5.039720770839918,
      -1.0397207708399179
    ]
  ]
}
```

## Hotelling Mean Vector Evidence Report

USD 19.00 per job.

Reconcile a one-sample mean vector, covariance and Hotelling T-squared/F reference statistic. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. One-sample T²=n*(mean-mu0)-transpose*S-inverse*(mean-mu0), n>p. Sample covariance positive definite with eigenvalue ratio>1e-10. F=(n-p)T²/[p(n-1)] is a normal-population reference statistic; no p-value, rejection or normality verification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [online.stat.psu.edu](https://online.stat.psu.edu/stat505/Lesson07). No endorsement is implied.

Example input:

```json
{
  "observations": [
    [
      0,
      0
    ],
    [
      2,
      0
    ],
    [
      0,
      2
    ],
    [
      2,
      2
    ]
  ],
  "hypothesizedMean": [
    0,
    0
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/sampleMean": [
    1,
    1
  ],
  "/sampleCovariance": [
    [
      1.3333333333333333,
      0
    ],
    [
      0,
      1.3333333333333333
    ]
  ],
  "/tSquared": 6,
  "/fStatistic": 2,
  "/numeratorDf": 2,
  "/denominatorDf": 2
}
```

## Canonical Correlation Analysis Report

USD 19.00 per job.

Compare paired feature views through centered canonical correlations and shared variation dimensions. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Paired rows n>p+q, each view p,q<=8 and positive definite centered covariance ratio>1e-10. Whiten cross-covariance, then singular values; output min(p,q) canonical correlations clamped only within floating tolerance of[0,1]. No weights for degenerate axes, significance or out-of-sample claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [stat.ethz.ch](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/cancor.html). No endorsement is implied.

Example input:

```json
{
  "x": [
    [
      0
    ],
    [
      1
    ],
    [
      2
    ],
    [
      3
    ]
  ],
  "y": [
    [
      1
    ],
    [
      3
    ],
    [
      5
    ],
    [
      7
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/xMeans": [
    1.5
  ],
  "/yMeans": [
    4
  ],
  "/canonicalCorrelations": [
    1
  ],
  "/squaredCorrelations": [
    1
  ]
}
```

## Multivariate Linear Response Fit Report

USD 19.00 per job.

Fit one supplied design to multiple responses and reconcile residual covariance and fitted values. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Unweighted ordinary least squares with automatically added intercept; paired rows n>predictorCount+1, <=8 predictors/responses. Normal-equation Gram positive definite ratio>1e-10; rescale/center caller units when rejected. Residual covariance divisor residualDf; constant-response R² isnull. No intervals, regularization or forecast validation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [stat.ethz.ch](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/lm.html). No endorsement is implied.

Example input:

```json
{
  "predictors": [
    [
      0
    ],
    [
      1
    ],
    [
      2
    ]
  ],
  "responses": [
    [
      1,
      2
    ],
    [
      3,
      1
    ],
    [
      5,
      0
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coefficients": [
    [
      1,
      2
    ],
    [
      2,
      -1
    ]
  ],
  "/fitted": [
    [
      1,
      2
    ],
    [
      3,
      1
    ],
    [
      5,
      0
    ]
  ],
  "/residualCovariance": [
    [
      0,
      0
    ],
    [
      0,
      0
    ]
  ],
  "/rSquared": [
    1,
    1
  ],
  "/residualDf": 1
}
```

## Minimum Covariance Subset Report

USD 19.00 per job.

Find a bounded exhaustive minimum-volume covariance subset and its unscaled location/scatter. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Enumerate every size-h subset (at most4096); p<=4,n<=14,h>p. Objective log determinant of ordinary sample covariance divisor h-1. Any minimum numerically singular subset rejects; require eigenvalue ratio>1e-10. Logdet ties within1e-10 choose lexical indices. Raw subset only, no MCD consistency scaling/reweighting or anomaly verdict. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [stat.ethz.ch](https://stat.ethz.ch/CRAN/web/packages/robustbase/vignettes/fastMcd-kmini.pdf). No endorsement is implied.

Example input:

```json
{
  "observations": [
    [
      0
    ],
    [
      1
    ],
    [
      2
    ],
    [
      100
    ]
  ],
  "subsetSize": 3
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/selectedIndices": [
    0,
    1,
    2
  ],
  "/location": [
    1
  ],
  "/covariance": [
    [
      1
    ]
  ],
  "/logDeterminant": 0,
  "/subsetsExamined": 4
}
```

## Paired Landmark Procrustes Map Report

USD 19.00 per job.

Fit a proper planar rotation, translation and optional uniform scale between paired landmarks. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Paired 2D landmarks, same row count and positive centered source spread. Proper rotation only, no reflection; optional nonnegative uniform scale. Unit scale when fitScalefalse. Zero cross-covariance chooses rotation0; target collapse may give scale0. Equal weights, no correspondence search, outlier rejection or geospatial projection. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.stanford.edu](https://web.stanford.edu/class/cs273/refs/umeyama.pdf). No endorsement is implied.

Example input:

```json
{
  "source": [
    [
      0,
      0
    ],
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ],
  "target": [
    [
      2,
      3
    ],
    [
      2,
      5
    ],
    [
      0,
      3
    ]
  ],
  "fitScale": true
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/rotationRadians": 1.5707963267948966,
  "/scale": 2,
  "/translation": [
    2,
    3
  ],
  "/mapped": [
    [
      2,
      3
    ],
    [
      2,
      5
    ],
    [
      0,
      3
    ]
  ],
  "/squaredError": 0,
  "/rmsPointError": 0
}
```

## Multivariate Energy Sample Evidence Report

USD 19.00 per job.

Compare two small multivariate samples with an energy distance and exhaustive label-permutation reference. One-time supplied-data descriptive model; no causal, predictive-performance or professional certification claim. Euclidean biased V-statistic D=2*mean cross-distance-mean within A-mean within B, self-pairs included; scaled by n*m/(n+m). Enumerate all index-label splits of fixed sample sizes (<=924), ties extreme with distance-scale relative tolerance1e-12. Exchangeability required for the reference; no asymptotics, automatic decision or causal claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [stat.ethz.ch](https://stat.ethz.ch/CRAN/web/packages/energy/energy.pdf). No endorsement is implied.

Example input:

```json
{
  "sampleA": [
    [
      0
    ],
    [
      0
    ]
  ],
  "sampleB": [
    [
      1
    ],
    [
      1
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/energyDistance": 2,
  "/scaledStatistic": 2,
  "/permutations": 6,
  "/extremePermutations": 2,
  "/permutationPValue": 0.3333333333333333
}
```

## Candidate D-Optimal Run Selection

USD 19.00 per job.

Choose a full-rank experimental run subset for a supplied linear model. Exhaustive subsets of at most fourteen candidate model rows; supplied columns include any intercept. No replicate selection, randomization or safe operating-range advice. Numerically rank-deficient information matrices are rejected. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.itl.nist.gov](https://www.itl.nist.gov/div898/handbook/pri/section5/pri521.htm). No endorsement is implied.

Example input:

```json
{
  "modelRows": [
    [
      1,
      -1
    ],
    [
      1,
      0
    ],
    [
      1,
      1
    ]
  ],
  "runCount": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/selectedIndices": [
    0,
    2
  ],
  "/informationDeterminant": 4,
  "/evaluatedSubsets": 3
}
```

## Maximin Candidate Coverage Plan

USD 19.00 per job.

Select a run subset that maximizes its closest pairwise distance. Exhaustive search over supplied unit-cube coordinates, at most fourteen candidates. Squared Euclidean distance; earliest lexicographic subset resolves exact ties. Coverage criterion only, not response-model optimality. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.qmc.LatinHypercube.html). No endorsement is implied.

Example input:

```json
{
  "points": [
    [
      0
    ],
    [
      0.4
    ],
    [
      1
    ]
  ],
  "runCount": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/selectedIndices": [
    0,
    2
  ],
  "/minimumSquaredDistance": 1
}
```

## Latin Hypercube Coordinate Plan

USD 19.00 per job.

Prepare a stratified multidimensional coordinate plan from approved stratum permutations. Centered deterministic coordinates with one point in each stratum per dimension. Caller supplies permutations; no random number generation, optimization or statistical independence claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.qmc.LatinHypercube.html). No endorsement is implied.

Example input:

```json
{
  "strataByDimension": [
    [
      0,
      1
    ],
    [
      1,
      0
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coordinates": [
    [
      0.25,
      0.75
    ],
    [
      0.75,
      0.25
    ]
  ],
  "/runs": 2
}
```

## Plackett–Burman Screening Plan

USD 19.00 per job.

Prepare a twelve-run main-effect screening design and its orthogonality checks. Fixed twelve-run NIST pattern for one through eleven named factors. Coded levels only; main effects can be confounded with interactions. Execution order is deterministic and must be approved separately. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.itl.nist.gov](https://www.itl.nist.gov/div898/handbook/pri/section3/pri335.htm). No endorsement is implied.

Example input:

```json
{
  "factors": [
    "Temperature",
    "Pressure"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/columnSums": [
    0,
    0
  ],
  "/crossProducts": [
    [
      12,
      0
    ],
    [
      0,
      12
    ]
  ]
}
```

## Three-Factor Box–Behnken Plan

USD 19.00 per job.

Prepare edge-midpoint and center coordinates for a three-factor response-surface study. Exactly three named factors, twelve edge runs and caller-selected center repeats. Coded coordinates only; no model fitting, run randomization or physical safety recommendation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.itl.nist.gov](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm). No endorsement is implied.

Example input:

```json
{
  "factors": [
    "A",
    "B",
    "C"
  ],
  "centerRuns": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/runCount": 13,
  "/codedRuns/12": [
    0,
    0,
    0
  ]
}
```

## Multiple Comparison Adjustment

USD 19.00 per job.

Compare family-wise and false-discovery adjustments for supplied p-values. Bonferroni, Holm, Benjamini–Hochberg and Benjamini–Yekutieli adjusted p-values. BH assumes independence or suitable positive dependence; BY covers arbitrary dependence. Input p-values and test validity remain the caller’s responsibility. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.stats.multitest.multipletests.html). No endorsement is implied.

Example input:

```json
{
  "pvalues": [
    0.01,
    0.04,
    0.03
  ],
  "alpha": 0.05
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/adjustments/0/holm": 0.03,
  "/adjustments/1/benjaminiHochberg": 0.04,
  "/adjustments/2/holm": 0.06
}
```

## Independent Evidence Combination

USD 19.00 per job.

Combine independent continuous-null p-values using Fisher and Tippett methods. Independent, valid continuous p-values are required; discrete or dependent inputs do not inherit the stated null calibration. Fisher uses its even-degree chi-square survival formula. No causal or business verdict. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.combine_pvalues.html). No endorsement is implied.

Example input:

```json
{
  "pvalues": [
    1,
    1
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/fisherStatistic": 0,
  "/degreesOfFreedom": 4,
  "/fisherP": 1,
  "/tippettP": 1
}
```

## Random-Effects Evidence Summary

USD 19.00 per job.

Combine compatible effect estimates with their supplied sampling variances. DerSimonian–Laird nonnegative between-study variance, inverse-variance fixed and random summaries, standard error and heterogeneity. No small-sample correction, confidence interval or study-quality assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.stats.meta_analysis.combine_effects.html). No endorsement is implied.

Example input:

```json
{
  "studies": [
    {
      "effect": 1,
      "variance": 1
    },
    {
      "effect": 3,
      "variance": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/fixedEffect": 2,
  "/randomEffect": 2,
  "/tauSquared": 1,
  "/heterogeneityQ": 2,
  "/iSquared": 0.5,
  "/randomStandardError": 1
}
```

## Two-Arm Normal Power Scenarios

USD 19.00 per job.

Compare two-sided normal-test power across equal-sized study arms. Known common standard deviation represented by standardized effect; supplied nonnegative normal critical value. Independent equal arms, normal approximation only, no t-test, dropout or allocation-ratio adjustment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.stats.power.NormalIndPower.html). No endorsement is implied.

Example input:

```json
{
  "standardizedEffect": 0,
  "criticalZ": 0,
  "perArmSampleSizes": [
    2,
    10
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/scenarios/0/power": 1,
  "/scenarios/1/power": 1,
  "/scenarios/0/noncentrality": 0
}
```

## Blocked Allocation Possibilities

USD 19.00 per job.

Enumerate treatment assignments satisfying caller-defined block totals. Deterministic enumeration of every binary allocation within each block, up to five thousand combined assignments. No random draw, participant processing or assignment execution. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.itl.nist.gov](https://www.itl.nist.gov/div898/handbook/pri/section3/pri332.htm). No endorsement is implied.

Example input:

```json
{
  "blocks": [
    {
      "size": 2,
      "treated": 1
    },
    {
      "size": 2,
      "treated": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/assignmentCount": 4,
  "/assignments": [
    [
      1,
      0,
      1,
      0
    ],
    [
      1,
      0,
      0,
      1
    ],
    [
      0,
      1,
      1,
      0
    ],
    [
      0,
      1,
      0,
      1
    ]
  ]
}
```

## Seasonal Holt–Winters Replay

USD 19.00 per job.

Replay additive seasonal smoothing and prepare a bounded forecast. Fixed supplied smoothing parameters; first-season mean, second-season mean difference divided by period and centered first-season seasonal initialization. The gamma input is the conventional gamma-star weight using observation minus updated level. At least two complete seasons. No automatic parameter fitting or prediction interval. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [otexts.com](https://otexts.com/fpp3/exponential-smoothing.html). No endorsement is implied.

Example input:

```json
{
  "values": [
    1,
    3,
    1,
    3
  ],
  "period": 2,
  "alpha": 0.5,
  "beta": 0.5,
  "gamma": 0.5,
  "horizon": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/forecasts": [
    1,
    3
  ],
  "/squaredError": 0,
  "/level": 2
}
```

## Intermittent Demand Probability Forecast

USD 19.00 per job.

Track demand occurrence separately from positive demand size. Teunter–Syntetos–Babai updates with caller-supplied initial size and probability. Probability updates every period, size only on positive demand. Forecasts are constant conditional means, not stock prescriptions or intervals. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doi.org](https://doi.org/10.1016/j.ejor.2011.05.018). No endorsement is implied.

Example input:

```json
{
  "demand": [
    0,
    4,
    0
  ],
  "sizeAlpha": 0.5,
  "occurrenceBeta": 0.5,
  "initialSize": 4,
  "initialProbability": 0.5,
  "horizon": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/updatedForecasts": [
    1,
    2.5,
    1.25
  ],
  "/forecasts": [
    1.25,
    1.25
  ]
}
```

## Autoregressive Moment Fit

USD 19.00 per job.

Estimate a bounded autoregressive model from supplied series moments. Demeaned Yule–Walker equations with biased autocovariances divided by n. Rejects singular models and constant input; forecasts use zero future innovations. No stationarity certification, model selection or prediction interval. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.yule_walker.html). No endorsement is implied.

Example input:

```json
{
  "values": [
    -1,
    1,
    -1,
    1
  ],
  "order": 1,
  "horizon": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coefficients": [
    -0.75
  ],
  "/mean": 0,
  "/innovationVariance": 0.4375,
  "/forecasts": [
    -0.75
  ]
}
```

## ARMA Innovation Replay

USD 19.00 per job.

Replay supplied autoregressive and moving-average coefficients against observed data. Zero observations and innovations before the series; supplied intercept is the recursion constant, not the unconditional mean. No coefficient estimation, root stability guarantee or uncertainty interval. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/tsa.html). No endorsement is implied.

Example input:

```json
{
  "values": [
    1,
    2,
    3,
    4
  ],
  "autoregressive": [
    1
  ],
  "movingAverage": [],
  "intercept": 0,
  "horizon": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/innovations": [
    1,
    1,
    1,
    1
  ],
  "/forecasts": [
    4,
    4
  ],
  "/squaredError": 4
}
```

## Classical Seasonal Components

USD 19.00 per job.

Separate a supplied series into centered trend, seasonal pattern and residuals. Additive centered moving-average decomposition; even periods use half-weighted window endpoints. At least two complete seasons; trend and residual endpoints remain null. No extrapolation or automatic period selection. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.tsa.seasonal.seasonal_decompose.html). No endorsement is implied.

Example input:

```json
{
  "values": [
    1,
    3,
    1,
    3
  ],
  "period": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/trend": [
    null,
    2,
    2,
    null
  ],
  "/seasonalPattern": [
    -1,
    1
  ],
  "/residual": [
    null,
    0,
    0,
    null
  ]
}
```

## Residual Serial-Correlation Evidence

USD 19.00 per job.

Summarize cumulative Ljung–Box residual diagnostics by lag. Demeaned biased autocorrelations; Q=n(n+2) sum rho(k)^2/(n-k). Degrees of freedom subtract supplied fitted-parameter count, clamped at zero. Statistics only; no p-values, critical values or automatic adequacy verdict. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.stats.diagnostic.acorr_ljungbox.html). No endorsement is implied.

Example input:

```json
{
  "residuals": [
    1,
    -1,
    1,
    -1
  ],
  "maxLag": 1,
  "fittedParameters": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/lags/0/autocorrelation": -0.75,
  "/lags/0/qStatistic": 4.5,
  "/lags/0/degreesOfFreedom": 1
}
```

## Augmented Lagged-Level Evidence

USD 19.00 per job.

Estimate the lagged-level coefficient and its regression diagnostic. Constant-only ADF regression with a caller-selected number of lagged differences. Full-rank OLS and positive residual degrees of freedom required. Zero standard errors yield null t-statistic. No ordinary t-distribution p-value, stationarity verdict or critical-value approximation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.adfuller.html). No endorsement is implied.

Example input:

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

Selected expected result fields (JSON pointers):

```json
{
  "/laggedLevelCoefficient": -2,
  "/intercept": 1,
  "/tStatistic": null,
  "/residualDegreesOfFreedom": 3
}
```

## Level Stationarity Statistic

USD 19.00 per job.

Calculate cumulative-residual evidence against a constant-level model. Demeaned residuals, Bartlett/Newey–West long-run variance and supplied bandwidth. Constant or degenerate long-run variance is rejected. No p-value, critical-value interpolation or automatic stationarity decision. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.statsmodels.org](https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.kpss.html). No endorsement is implied.

Example input:

```json
{
  "values": [
    1,
    -1,
    1,
    -1
  ],
  "bandwidth": 0
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/statistic": 0.125,
  "/partialSumEnergy": 0.125,
  "/longRunVariance": 1
}
```

## Multiple Mean-Change Segmentation

USD 19.00 per job.

Find a globally least-cost piecewise-constant description of supplied observations. Dynamic programming minimizes within-segment squared error plus a caller-specified penalty per change, subject to minimum segment length. Up to 128 observations; no automatic penalty calibration, causal explanation or future-change prediction. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.lancaster.ac.uk](https://www.lancaster.ac.uk/~romano/teaching/2425MATH337/3_multiple_changes.html). No endorsement is implied.

Example input:

```json
{
  "values": [
    0,
    0,
    10,
    10,
    0,
    0
  ],
  "minimumSegment": 2,
  "changePenalty": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/boundaries": [
    2,
    4
  ],
  "/squaredError": 0,
  "/penalizedCost": 2
}
```

## Seasonal Rank-Trend Evidence

USD 19.00 per job.

Compare within-season observation pairs while accounting for exact ties. Regular complete series grouped by position modulo period. Tie-adjusted seasonal score variances are summed assuming zero covariance across seasons; continuity-corrected z only, no significance verdict or serial-dependence correction. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [pubs.usgs.gov](https://pubs.usgs.gov/wsp/2190/report.pdf). No endorsement is implied.

Example input:

```json
{
  "values": [
    1,
    10,
    2,
    20,
    3,
    30
  ],
  "period": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/score": 6,
  "/variance": 7.333333333333333
}
```

## Capacity and Preference Match

USD 19.00 per job.

Match applicants to capacity-limited positions using declared priorities. Applicant-proposing deferred acceptance with strict preferences and complete position priorities. Applicants may omit unacceptable positions; zero capacity is allowed. No external placement, legal eligibility or transferable payment mechanism. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [stanford.edu](https://stanford.edu/~alroth/papers/GaleandShapley.revised.IJGT.pdf). No endorsement is implied.

Example input:

```json
{
  "applicants": [
    {
      "id": "A",
      "preferences": [
        "X",
        "Y"
      ]
    },
    {
      "id": "B",
      "preferences": [
        "X",
        "Y"
      ]
    }
  ],
  "positions": [
    {
      "id": "X",
      "capacity": 1,
      "priority": [
        "B",
        "A"
      ]
    },
    {
      "id": "Y",
      "capacity": 1,
      "priority": [
        "A",
        "B"
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/assignments": [
    {
      "applicant": "A",
      "position": "Y"
    },
    {
      "applicant": "B",
      "position": "X"
    }
  ],
  "/unmatched": []
}
```

## Endowment Trading-Cycle Plan

USD 19.00 per job.

Reallocate one endowed object per participant through preference cycles. Strict complete preferences and unique existing endowments. Iteratively executes a detected top-trading cycle in the supplied scenario only; cycles in the same logical stage may be numbered separately. No real ownership transfer or payment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.stanford.edu](https://web.stanford.edu/~alroth/papers/bostonMay182006.pdf). No endorsement is implied.

Example input:

```json
{
  "agents": [
    {
      "id": "A",
      "endowment": "X",
      "preferences": [
        "Y",
        "X"
      ]
    },
    {
      "id": "B",
      "endowment": "Y",
      "preferences": [
        "X",
        "Y"
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/allocation": [
    {
      "agent": "A",
      "object": "Y",
      "round": 1
    },
    {
      "agent": "B",
      "object": "X",
      "round": 1
    }
  ],
  "/roundCount": 1
}
```

## Probabilistic Serial Share Plan

USD 19.00 per job.

Allocate divisible probability shares under strict ordinal preferences. Equal numbers of participants and unit-capacity objects. All participants consume their most preferred remaining object at equal speed through time one. Numerical shares only; no lottery draw or indivisible assignment execution. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.stanford.edu](https://web.stanford.edu/~niederle/RandomAssignment.pdf). No endorsement is implied.

Example input:

```json
{
  "objects": [
    "X",
    "Y"
  ],
  "agents": [
    {
      "id": "A",
      "preferences": [
        "X",
        "Y"
      ]
    },
    {
      "id": "B",
      "preferences": [
        "X",
        "Y"
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/shares": [
    {
      "agent": "A",
      "fractions": [
        0.5,
        0.5
      ]
    },
    {
      "agent": "B",
      "fractions": [
        0.5,
        0.5
      ]
    }
  ],
  "/objectTotals": [
    1,
    1
  ],
  "/completionTime": 1
}
```

## Random-Priority Allocation Distribution

USD 19.00 per job.

Enumerate the allocation distribution across all priority orders. Complete strict preferences, one object per participant and at most seven participants. Every priority permutation is equally weighted; no random draw, assignment execution or equality-of-utility guarantee. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.stanford.edu](https://web.stanford.edu/~niederle/RandomAssignment.pdf). No endorsement is implied.

Example input:

```json
{
  "objects": [
    "X",
    "Y"
  ],
  "agents": [
    {
      "id": "A",
      "preferences": [
        "X",
        "Y"
      ]
    },
    {
      "id": "B",
      "preferences": [
        "X",
        "Y"
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/priorityOrderCount": 2,
  "/shares/0/assignmentCounts": [
    1,
    1
  ],
  "/shares/1/probabilities": [
    0.5,
    0.5
  ]
}
```

## Sealed-Bid Rule Comparison

USD 19.00 per job.

Compare first-price and second-price outcomes for supplied bids. One item, integer values in a common caller-defined unit and seller reserve. Input order resolves tied bids. Outputs are hypothetical clearing amounts, not payment requests, market valuations or strategic recommendations. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/14-12-economic-applications-of-game-theory-fall-2025/resources/mit14_12f25_lec18_1080p_mp4/). No endorsement is implied.

Example input:

```json
{
  "bids": [
    {
      "id": "A",
      "value": 10
    },
    {
      "id": "B",
      "value": 7
    }
  ],
  "reserve": 5
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/winner": "A",
  "/firstPrice": 10,
  "/secondPrice": 7,
  "/eligibleBids": 2
}
```

## Multiunit Bid Clearing Comparison

USD 19.00 per job.

Compare pay-as-bid and highest-rejected-bid uniform clearing. Identical units, nonincreasing integer marginal bids and reserve. Input bidder order then marginal-unit order resolves ties. This is a submitted-bid scenario; no strategy-proofness, live auction or actual charge. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/14-16-strategy-and-information-spring-2016/88a1631b5ed6512f32a2ef239830322a_MIT14_16S16_Bayesian.pdf). No endorsement is implied.

Example input:

```json
{
  "bidders": [
    {
      "id": "A",
      "unitBids": [
        10,
        6
      ]
    },
    {
      "id": "B",
      "unitBids": [
        8,
        4
      ]
    }
  ],
  "units": 2,
  "reserve": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/allocatedUnits": 2,
  "/uniformUnitPrice": 6,
  "/payAsBidRevenue": 18,
  "/uniformRevenue": 12
}
```

## Bundle-Bid Allocation Scenario

USD 19.00 per job.

Find the highest-value compatible selection of supplied package bids. Exhaustive selection over at most sixteen bids and twelve items, with disjoint item bundles and at most one accepted bid per bidder. Maximizes submitted integer bid value; no VCG payment calculation or allocation execution. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [people.csail.mit.edu](https://people.csail.mit.edu/costis/6853fa2011/). No endorsement is implied.

Example input:

```json
{
  "items": [
    "X",
    "Y"
  ],
  "bids": [
    {
      "id": "AX",
      "bidder": "A",
      "items": [
        "X"
      ],
      "value": 6
    },
    {
      "id": "BY",
      "bidder": "B",
      "items": [
        "Y"
      ],
      "value": 6
    },
    {
      "id": "CXY",
      "bidder": "C",
      "items": [
        "X",
        "Y"
      ],
      "value": 10
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/acceptedBidIds": [
    "AX",
    "BY"
  ],
  "/totalBidValue": 12,
  "/allocatedItems": [
    "X",
    "Y"
  ]
}
```

## Stable Roommate Pairing Scenario

USD 19.00 per job.

Find a stable complete pairing or establish none exists in a bounded preference scenario. Complete strict preferences for an even set of at most ten participants. Exhaustively checks pairings for mutually preferred blocking pairs. No ties, incomplete lists, external assignment or promise that a stable pairing always exists. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.dcs.gla.ac.uk](https://www.dcs.gla.ac.uk/research/algorithms/workshop/matchup.pdf). No endorsement is implied.

Example input:

```json
{
  "people": [
    {
      "id": "A",
      "preferences": [
        "B",
        "C",
        "D"
      ]
    },
    {
      "id": "B",
      "preferences": [
        "A",
        "C",
        "D"
      ]
    },
    {
      "id": "C",
      "preferences": [
        "D",
        "A",
        "B"
      ]
    },
    {
      "id": "D",
      "preferences": [
        "C",
        "A",
        "B"
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/stable": true,
  "/pairs": [
    {
      "first": "A",
      "second": "B"
    },
    {
      "first": "C",
      "second": "D"
    }
  ]
}
```

## Assigned-Object Envy Review

USD 19.00 per job.

Inspect strict envy and potential trading cycles in an existing allocation. Supplied cardinal utilities and one assigned object per participant. Returns strict envy edges and one cycle when present; absence of a strict cycle does not establish full Pareto efficiency under weak improvements. No reassignment or utility comparability across participants. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.stanford.edu](https://web.stanford.edu/~alroth/papers/bostonMay182006.pdf). No endorsement is implied.

Example input:

```json
{
  "objects": [
    "X",
    "Y"
  ],
  "agents": [
    {
      "id": "A",
      "assigned": "X",
      "utilities": [
        1,
        2
      ]
    },
    {
      "id": "B",
      "assigned": "Y",
      "utilities": [
        2,
        1
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/envyFree": false,
  "/strictImprovementCycle": [
    "A",
    "B"
  ]
}
```

## Cooperative Cost Allocation Check

USD 19.00 per job.

Check a proposed cost split against every supplied coalition’s standalone cost. Complete integer coalition-cost table indexed by bit mask, including zero empty-coalition cost. Core membership requires exact grand-total equality and no coalition allocated more than its standalone cost. Does not compute a Shapley allocation or recommend legal cost-sharing terms. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [dspace.mit.edu](https://dspace.mit.edu/server/api/core/bitstreams/04102157-57eb-4498-ae43-3de67b045d6f/content). No endorsement is implied.

Example input:

```json
{
  "players": [
    "A",
    "B"
  ],
  "coalitionCosts": [
    0,
    7,
    7,
    10
  ],
  "allocation": [
    5,
    5
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/efficient": true,
  "/inCore": true,
  "/violations": []
}
```

## Capacity-Constrained Transport Plan

USD 19.00 per job.

Find least-cost shipments subject to supplied source, demand and route capacities. Integer units, nonnegative integer unit costs and at most 128 demand units. Successive shortest residual paths find minimum cost at the maximum shippable flow; infeasible demand is reported with partial shipments. No freight booking or real capacity verification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [developers.google.com](https://developers.google.com/optimization/flow/mincostflow). No endorsement is implied.

Example input:

```json
{
  "supply": [
    2,
    2
  ],
  "demand": [
    1,
    3
  ],
  "unitCosts": [
    [
      1,
      5
    ],
    [
      2,
      1
    ]
  ],
  "routeCapacities": [
    [
      4,
      4
    ],
    [
      4,
      4
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/shipments": [
    [
      1,
      1
    ],
    [
      0,
      2
    ]
  ],
  "/totalCost": 8,
  "/unmet": 0
}
```

## Facility Opening and Supply Scenario

USD 19.00 per job.

Compare facility-opening choices with their capacity and distribution cost. Enumerates at most six candidate facilities and solves each feasible integer transport subproblem. Fixed opening costs plus linear shipping, splittable demand and at most forty demand units. No geographic search, construction advice or real opening action. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.ocw.mit.edu](https://www.ocw.mit.edu/courses/15-094j-systems-optimization-models-and-computation-sma-5223-spring-2004/4eba7929cbf04a752ab0c9fefd26b08e_lec8_sma_tsp.pdf). No endorsement is implied.

Example input:

```json
{
  "facilities": [
    {
      "id": "A",
      "capacity": 3,
      "openingCost": 5
    },
    {
      "id": "B",
      "capacity": 3,
      "openingCost": 1
    }
  ],
  "demand": [
    2
  ],
  "shippingUnitCosts": [
    [
      1
    ],
    [
      4
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/openFacilities": [
    "A"
  ],
  "/totalCost": 7,
  "/shipments": [
    [
      2
    ],
    [
      0
    ]
  ]
}
```

## Integer Product Mix Plan

USD 19.00 per job.

Find a highest-contribution production mix under shared resource constraints. Exhaustive bounded integer quantities, nonnegative unit contributions and resource use. Up to two hundred thousand quantity combinations; reported resource totals witness feasibility. No demand forecast, inventory policy, fractional production or actual scheduling. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [developers.google.com](https://developers.google.com/optimization/pack/knapsack). No endorsement is implied.

Example input:

```json
{
  "products": [
    {
      "id": "A",
      "maxUnits": 3,
      "unitProfit": 5,
      "resourceUse": [
        2
      ]
    },
    {
      "id": "B",
      "maxUnits": 5,
      "unitProfit": 2,
      "resourceUse": [
        1
      ]
    }
  ],
  "resourceCapacities": [
    5
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/quantities": [
    {
      "product": "A",
      "units": 2
    },
    {
      "product": "B",
      "units": 1
    }
  ],
  "/resourceUse": [
    5
  ],
  "/profit": 12
}
```

## Precedence Line Station Balance

USD 19.00 per job.

Minimize station count under a supplied cycle time and task precedence. Exact subset dynamic programming for at most ten indivisible deterministic tasks. Predecessors may share a station in a valid local order. A task longer than the cycle is rejected. No parallel equipment, ergonomic, equipment-safety or variability analysis. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/2.810/www/files/lectures/lec7-assembly-whitney-2016.pdf). No endorsement is implied.

Example input:

```json
{
  "tasks": [
    {
      "id": "A",
      "duration": 2,
      "predecessors": []
    },
    {
      "id": "B",
      "duration": 2,
      "predecessors": [
        "A"
      ]
    },
    {
      "id": "C",
      "duration": 2,
      "predecessors": []
    }
  ],
  "cycleTime": 4
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/stationCount": 2
}
```

## Cyclic Shift Coverage Plan

USD 19.00 per job.

Choose low-cost repeating shift starts that cover every period’s stated need. Homogeneous staff, fixed consecutive shift length and integer starts on a repeating cycle. Exact enumeration within a bounded scenario, no named-worker roster, labor-law check or automatic assignment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/15-057-systems-optimization-spring-2003/). No endorsement is implied.

Example input:

```json
{
  "requirements": [
    1,
    1,
    1
  ],
  "shiftLength": 2,
  "maxStartsPerPeriod": 1,
  "startCosts": [
    1,
    2,
    3
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/starts": [
    1,
    1,
    0
  ],
  "/coverage": [
    1,
    2,
    1
  ],
  "/totalCost": 3
}
```

## Setup and Deadline Machine Plan

USD 19.00 per job.

Compare task sequences using release times, changeovers and weighted lateness. One nonpreemptive machine and at most eight jobs. Setup starts only after both machine availability and job release; objective is total weighted tardiness, then makespan. Exhaustive sequence search; no live dispatch or machine-safety assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [developers.google.com](https://developers.google.com/optimization/scheduling/job_shop). No endorsement is implied.

Example input:

```json
{
  "jobs": [
    {
      "id": "A",
      "duration": 2,
      "release": 0,
      "due": 2,
      "tardinessWeight": 1
    },
    {
      "id": "B",
      "duration": 1,
      "release": 0,
      "due": 4,
      "tardinessWeight": 1
    }
  ],
  "initialSetups": [
    0,
    0
  ],
  "changeovers": [
    [
      0,
      0
    ],
    [
      0,
      0
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/order": [
    "A",
    "B"
  ],
  "/weightedTardiness": 0,
  "/makespan": 3
}
```

## Project Resource Leveling Scenario

USD 19.00 per job.

Find low-peak resource timing within approved task windows and dependencies. Integer start times, deterministic durations and renewable resource demand. Exact bounded enumeration minimizes peak load then squared load, with no fixed capacity ceiling. No calendar, equipment reservation or execution; infeasible windows return no plan. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [developers.google.com](https://developers.google.com/optimization/scheduling/job_shop). No endorsement is implied.

Example input:

```json
{
  "tasks": [
    {
      "id": "A",
      "duration": 2,
      "resource": 2,
      "earliestStart": 0,
      "latestStart": 2,
      "predecessors": []
    },
    {
      "id": "B",
      "duration": 2,
      "resource": 2,
      "earliestStart": 0,
      "latestStart": 2,
      "predecessors": []
    }
  ],
  "horizon": 4
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/peakLoad": 2,
  "/squaredLoad": 16,
  "/loads": [
    2,
    2,
    2,
    2
  ]
}
```

## Production and Inventory Smoothing

USD 19.00 per job.

Balance production, holding and production-change costs over a finite horizon. Integer capacity and demand, no shortages or backlogs, exact required ending inventory. Dynamic programming minimizes linear production and holding cost plus absolute change from the preceding period’s production. Up to eight periods; no live production scheduling. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/15-057-systems-optimization-spring-2003/resources/06productionplanningprint/). No endorsement is implied.

Example input:

```json
{
  "periods": [
    {
      "demand": 1,
      "capacity": 2,
      "unitCost": 1,
      "holdingCost": 1
    },
    {
      "demand": 2,
      "capacity": 2,
      "unitCost": 1,
      "holdingCost": 1
    }
  ],
  "initialInventory": 0,
  "finalInventory": 0,
  "initialProduction": 0,
  "changeCost": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/production": [
    1,
    2
  ],
  "/inventory": [
    0,
    0
  ],
  "/totalCost": 7
}
```

## Dependency-Constrained Project Portfolio

USD 19.00 per job.

Find a highest-value project subset that includes its prerequisites and fits a planning budget. Exhaustive selection of at most sixteen projects, integer cost/value and acyclic prerequisites. Maximizes supplied value, then minimizes spend. The budget is a planning input, not a limit on payments; no investment advice or project approval. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [developers.google.com](https://developers.google.com/optimization/pack/knapsack). No endorsement is implied.

Example input:

```json
{
  "projects": [
    {
      "id": "A",
      "cost": 3,
      "value": 2,
      "predecessors": []
    },
    {
      "id": "B",
      "cost": 2,
      "value": 10,
      "predecessors": [
        "A"
      ]
    },
    {
      "id": "C",
      "cost": 3,
      "value": 8,
      "predecessors": []
    }
  ],
  "budget": 5
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/selectedProjects": [
    "A",
    "B"
  ],
  "/spent": 5,
  "/totalValue": 12
}
```

## Mixed Scenario Regret Plan

USD 19.00 per job.

Find a randomized decision mix that minimizes its worst expected scenario regret. Finite supplied payoff matrix, up to five decisions and eight scenarios. Enumerates linear-program vertices; regret compares expected payoff with the best pure decision in each scenario. Numerical solution, no scenario probabilities, realized loss guarantee, action execution or investment advice. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.mit.edu](https://www.mit.edu/~jaillet/general/rand_mmr_final.pdf). No endorsement is implied.

Example input:

```json
{
  "decisions": [
    "A",
    "B"
  ],
  "scenarioPayoffs": [
    [
      10,
      0
    ],
    [
      0,
      10
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/weights": [
    0.5,
    0.5
  ],
  "/expectedPayoffs": [
    5,
    5
  ],
  "/scenarioRegrets": [
    5,
    5
  ],
  "/maximumRegret": 5
}
```

## Custody and Seal Event Review

USD 19.00 per job.

Reconcile supplied custody transfers against the preceding custodian and seal. Chronological explicit events with unique asset references. Custodian or declared-seal mismatches are reported and excluded from state; a new seal is accepted only with a consistent handoff. No physical verification, cryptographic evidence, ownership determination or EPCIS certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.gs1.org](https://www.gs1.org/standards/epcis-and-cbv-implementation-guideline/current-standardd). No endorsement is implied.

Example input:

```json
{
  "assets": [
    {
      "id": "Box",
      "custodian": "A",
      "seal": "S1"
    }
  ],
  "events": [
    {
      "id": "E1",
      "asset": "Box",
      "at": 1,
      "from": "A",
      "to": "B",
      "expectedSeal": "S1",
      "newSeal": "S2"
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/assets": [
    {
      "asset": "Box",
      "custodian": "B",
      "seal": "S2"
    }
  ],
  "/acceptedEvents": 1,
  "/findings": []
}
```

## Rental Return-to-Ready Ledger

USD 19.00 per job.

Reconcile asset rental, return, cleaning, inspection and release events. Initial assets are available. The declared sequence is rent → return → clean → inspect → release; later events must retain the active rental reference. Durations use caller-supplied monotonic time units. No booking, payment, inspection execution or equipment-safety judgment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.odoo.com](https://www.odoo.com/documentation/19.0/applications/sales/rental.html). No endorsement is implied.

Example input:

```json
{
  "assets": [
    "A"
  ],
  "events": [
    {
      "id": "E1",
      "asset": "A",
      "at": 1,
      "action": "rent",
      "rental": "R1"
    },
    {
      "id": "E2",
      "asset": "A",
      "at": 4,
      "action": "return",
      "rental": "R1"
    },
    {
      "id": "E3",
      "asset": "A",
      "at": 5,
      "action": "clean",
      "rental": "R1"
    },
    {
      "id": "E4",
      "asset": "A",
      "at": 6,
      "action": "inspect",
      "rental": "R1"
    },
    {
      "id": "E5",
      "asset": "A",
      "at": 7,
      "action": "release",
      "rental": "R1"
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/assets": [
    {
      "asset": "A",
      "status": "available",
      "currentRental": null
    }
  ],
  "/completedCycles": [
    {
      "asset": "A",
      "rental": "R1",
      "rentalDuration": 3,
      "turnaroundDuration": 3
    }
  ]
}
```

## Consignment Stock and Proceeds Ledger

USD 19.00 per job.

Track owner-attributed consigned quantities and scenario proceeds. Receipts, sales, unsold returns and sale returns use one fixed unit sale price per lot. Sale returns cannot exceed net sales; owner references must match. Exact integer-string proceeds and half-up commission on cumulative net sales. No legal ownership verification, tax or remittance. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.odoo.com](https://www.odoo.com/documentation/19.0/applications/inventory_and_mrp/inventory/shipping_receiving/daily_operations/owned_stock.html). No endorsement is implied.

Example input:

```json
{
  "lots": [
    {
      "id": "L",
      "owner": "Owner",
      "initialQuantity": 10,
      "unitSaleMinor": "100",
      "commissionBasisPoints": 1000
    }
  ],
  "events": [
    {
      "id": "E1",
      "lot": "L",
      "at": 1,
      "owner": "Owner",
      "action": "sell",
      "quantity": 3
    },
    {
      "id": "E2",
      "lot": "L",
      "at": 2,
      "owner": "Owner",
      "action": "sale-return",
      "quantity": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/lots/0/onConsignment": 8,
  "/lots/0/netSold": 2,
  "/lots/0/grossMinor": "200",
  "/lots/0/commissionMinor": "20",
  "/lots/0/ownerProceedsMinor": "180"
}
```

## Reusable Container Pool Reconciliation

USD 19.00 per job.

Reconcile location stock, partial shipment receipts and recorded losses. Unique shipment references and chronological dispatch, receive and loss events. Receipts and losses cannot exceed outstanding shipment quantities. Conservation includes location stock plus in-transit and lost units. Supplied ledger only; no tracking feed or physical inventory certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ref.gs1.org](https://ref.gs1.org/standards/cbv/). No endorsement is implied.

Example input:

```json
{
  "locations": [
    {
      "id": "A",
      "initialStock": 10
    },
    {
      "id": "B",
      "initialStock": 0
    }
  ],
  "events": [
    {
      "id": "E1",
      "at": 1,
      "action": "dispatch",
      "shipment": "S",
      "from": "A",
      "to": "B",
      "quantity": 4
    },
    {
      "id": "E2",
      "at": 2,
      "action": "receive",
      "shipment": "S",
      "from": "A",
      "to": "B",
      "quantity": 3
    },
    {
      "id": "E3",
      "at": 3,
      "action": "lose",
      "shipment": "S",
      "from": "A",
      "to": "B",
      "quantity": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/locations": [
    {
      "location": "A",
      "stock": 6
    },
    {
      "location": "B",
      "stock": 3
    }
  ],
  "/lost": 1,
  "/conserved": true,
  "/shipments/0/inTransit": 0
}
```

## Usage Counter Rollover Review

USD 19.00 per job.

Reconcile cumulative readings across declared resets and single wraparounds. Strictly increasing sample times and values below the stated modulus. Assumes at most one wrap per non-reset interval; equal readings may hide full wraps. Reset intervals count only the post-reset reading and are explicitly incomplete. No meter verification or billing execution. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/info/rfc1982/). No endorsement is implied.

Example input:

```json
{
  "modulus": 100,
  "readings": [
    {
      "at": 0,
      "value": 90,
      "reset": false
    },
    {
      "at": 1,
      "value": 5,
      "reset": false
    },
    {
      "at": 2,
      "value": 8,
      "reset": false
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/observedUsage": 18,
  "/rollovers": 1,
  "/resets": 0,
  "/incompleteAcrossResets": false
}
```

## Usage Retry Reconciliation

USD 19.00 per job.

Separate first-seen usage, exact retries and conflicting reuse of an event key. Key uniqueness applies across the supplied ledger. The first operation and quantity define its fingerprint; exact duplicates count once, conflicting reuse is excluded and listed. No live deduplication store, concurrency claim, invoice or financial charge. IETF header work remains a draft, not a claimed implementation standard. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [datatracker.ietf.org](https://datatracker.ietf.org/doc/draft-ietf-httpapi-idempotency-key-header/). No endorsement is implied.

Example input:

```json
{
  "events": [
    {
      "key": "K1",
      "operation": "Compute",
      "quantity": 5
    },
    {
      "key": "K1",
      "operation": "Compute",
      "quantity": 5
    },
    {
      "key": "K1",
      "operation": "Compute",
      "quantity": 9
    },
    {
      "key": "K2",
      "operation": "Compute",
      "quantity": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/operations": [
    {
      "operation": "Compute",
      "countedQuantity": 7
    }
  ],
  "/acceptedEvents": 2,
  "/duplicateEvents": 1,
  "/conflicts/0/index": 2
}
```

## Declared Warranty Window Review

USD 19.00 per job.

Check claim dates and cause codes against supplied coverage terms. Inclusive start/end dates, optional void date effective from that date and a declared cause whitelist. Returns a contractual-window arithmetic classification only. No warranty-law interpretation, diagnosis, coverage decision, entitlement grant or customer contact. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.odoo.com](https://www.odoo.com/documentation/19.0/applications/inventory_and_mrp/repairs/repair_orders.html). No endorsement is implied.

Example input:

```json
{
  "assets": [
    {
      "id": "A",
      "startDate": "2026-01-01",
      "endDate": "2026-12-31",
      "voidDate": null
    }
  ],
  "coveredCauses": [
    "Defect"
  ],
  "claims": [
    {
      "id": "C",
      "asset": "A",
      "claimDate": "2026-12-31",
      "cause": "Defect"
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/claims/0/withinDeclaredCoverage": true,
  "/claims/0/reason": "within-declared-window",
  "/claims/0/daysUntilEnd": 0
}
```

## Work Order Transition Review

USD 19.00 per job.

Replay declared work-order transitions and required completion checks. Caller supplies finite states, allowed transitions, required check identifiers and initial order states. Source-state, rule and check failures are reported without updating state. A simple guarded ledger, not an SCXML interpreter or operational authorization system. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.w3.org](https://www.w3.org/TR/scxml/). No endorsement is implied.

Example input:

```json
{
  "states": [
    "Open",
    "Done"
  ],
  "rules": [
    {
      "from": "Open",
      "to": "Done",
      "requiredChecks": [
        "QC"
      ]
    }
  ],
  "orders": [
    {
      "id": "O",
      "state": "Open"
    }
  ],
  "events": [
    {
      "id": "E1",
      "order": "O",
      "at": 1,
      "from": "Open",
      "to": "Done",
      "checks": [
        "QC"
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/orders": [
    {
      "order": "O",
      "state": "Done"
    }
  ],
  "/acceptedEvents": 1,
  "/findings": []
}
```

## Receipt Inspection and Hold Ledger

USD 19.00 per job.

Reconcile quantities awaiting inspection, on hold, released, rejected and consumed. Receipts enter pending stock; hold/release-hold move between pending and held; inspection moves pending to released/rejected; consumption uses released stock only. Invalid overdraw events are excluded. Quantity reconciliation only, no actual inspection or product-quality approval. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.odoo.com](https://www.odoo.com/documentation/19.0/applications/inventory_and_mrp/quality/quality_management/quality_checks.html). No endorsement is implied.

Example input:

```json
{
  "lots": [
    {
      "id": "L",
      "initialPending": 5
    }
  ],
  "events": [
    {
      "id": "E1",
      "lot": "L",
      "at": 1,
      "action": "hold",
      "quantity": 2
    },
    {
      "id": "E2",
      "lot": "L",
      "at": 2,
      "action": "inspect-pass",
      "quantity": 3
    },
    {
      "id": "E3",
      "lot": "L",
      "at": 3,
      "action": "consume",
      "quantity": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/lots/0/pending": 0,
  "/lots/0/held": 2,
  "/lots/0/released": 2,
  "/lots/0/consumed": 1,
  "/lots/0/balanced": true
}
```

## Purchase Return and Credit Reconciliation

USD 19.00 per job.

Reconcile returned quantities with separately recorded credit quantities. Fixed order unit prices in one common minor unit, inclusive scenario tax rate and exact integer strings. Returns cannot exceed ordered quantities; credits cannot exceed accepted returns. Cumulative half-up gross rounding makes split credits reconcile. Does not issue credit notes, refunds, tax advice or payment requests. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.odoo.com](https://www.odoo.com/documentation/19.0/applications/finance/accounting/customer_invoices/credit_notes.html). No endorsement is implied.

Example input:

```json
{
  "orders": [
    {
      "id": "O",
      "quantity": 3,
      "unitPriceMinor": "100",
      "taxBasisPoints": 1000
    }
  ],
  "events": [
    {
      "id": "E1",
      "order": "O",
      "at": 1,
      "action": "return",
      "quantity": 2
    },
    {
      "id": "E2",
      "order": "O",
      "at": 2,
      "action": "credit",
      "quantity": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/orders/0/originalGrossMinor": "330",
  "/orders/0/recordedCreditMinor": "110",
  "/orders/0/remainingGrossMinor": "220",
  "/orders/0/returnedAwaitingCredit": 1
}
```

## Matrix Market Coordinate Decoder API

USD 3.00 per job.

Decode sparse Matrix Market coordinates into a canonical matrix. Matrix Market coordinate real, integer or pattern data; general or symmetric. Up to 64 rows and columns, 1024 entries and 16 KiB of text. Reject duplicate coordinates and extra records; symmetric input uses the lower triangle. Complex, skew and Hermitian forms excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [math.nist.gov](https://math.nist.gov/MatrixMarket/formats.html). No endorsement is implied.

Example input:

```json
{
  "text": "%%MatrixMarket matrix coordinate integer symmetric\n2 2 2\n1 1 3\n2 1 4\n"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/matrix": [
    [
      3,
      4
    ],
    [
      4,
      0
    ]
  ],
  "/storedEntries": 2
}
```

## FITS Header Card Profile API

USD 3.00 per job.

Interpret primary FITS logical header cards and declared array size. Up to 128 supplied 80-character ASCII cards. Require SIMPLE, BITPIX and NAXIS first, matching NAXISn dimensions and END last. Boolean and signed integer values only; 0–8 dimensions, each up to one billion, with bounded declared sample count. No full 2880-byte block, payload or extension qualification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [fits.gsfc.nasa.gov](https://fits.gsfc.nasa.gov/fits_standard.html). No endorsement is implied.

Example input:

```json
{
  "cards": [
    "SIMPLE  =                    T                                                  ",
    "BITPIX  =                    8                                                  ",
    "NAXIS   =                    0                                                  ",
    "END                                                                             "
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/bitpix": 8,
  "/dimensions": [],
  "/declaredDataBytes": "0"
}
```

## NRRD Header Profile API

USD 3.00 per job.

Parse a restricted NRRD header and reconcile declared sample layout. NRRD0005 header ending in a blank line, up to 16 KiB. Support listed scalar types, 1–8 dimensions and raw or ASCII encoding. Multibyte raw data requires byte order. Header metadata only; reject detached paths, unknown fields and supplied payload. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [teem.sourceforge.net](https://teem.sourceforge.net/nrrd/format.html). No endorsement is implied.

Example input:

```json
{
  "header": "NRRD0005\ntype: uchar\ndimension: 2\nsizes: 2 3\nencoding: raw\n\n"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/sizes": [
    2,
    3
  ],
  "/sampleCount": "6",
  "/decodedBinaryBytes": "6"
}
```

## VTK Legacy Grid Parser API

USD 3.00 per job.

Decode a small ASCII unstructured VTK grid into points and cells. Legacy VTK 3.0 ASCII UNSTRUCTURED_GRID, up to 128 points and 256 cells. Support vertex, line, triangle and tetrahedron types with exact connectivity lengths. Attributes, binary data, polyhedra and file loading excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.vtk.org](https://docs.vtk.org/en/latest/vtk_file_formats/vtk_legacy_file_format.html). No endorsement is implied.

Example input:

```json
{
  "text": "# vtk DataFile Version 3.0\nTriangle\nASCII\nDATASET UNSTRUCTURED_GRID\nPOINTS 3 float\n0 0 0 1 0 0 0 1 0\nCELLS 1 4\n3 0 1 2\nCELL_TYPES 1\n5\n"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/points": [
    [
      0,
      0,
      0
    ],
    [
      1,
      0,
      0
    ],
    [
      0,
      1,
      0
    ]
  ],
  "/cells": [
    [
      0,
      1,
      2
    ]
  ],
  "/cellTypes": [
    5
  ]
}
```

## PLY ASCII Mesh Parser API

USD 3.00 per job.

Decode the vertex and face subset of an ASCII PLY mesh. PLY 1.0 ASCII with ordered float x, y, z vertices and uchar/int vertex-index face lists. Up to 128 vertices, 256 faces and 32 vertices per face. Leading header comments allowed; other properties and elements excluded. No mesh-validity certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.graphics.stanford.edu](https://www.graphics.stanford.edu/data/3Dscanrep/). No endorsement is implied.

Example input:

```json
{
  "text": "ply\nformat ascii 1.0\nelement vertex 3\nproperty float x\nproperty float y\nproperty float z\nelement face 1\nproperty list uchar int vertex_indices\nend_header\n0 0 0\n1 0 0\n0 1 0\n3 0 1 2\n"
}
```

Selected expected result fields (JSON pointers):

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

## Binary STL Mesh Decoder API

USD 3.00 per job.

Decode binary STL triangle records into explicit vertices and stored normals. Exact binary STL length of 84 plus 50 bytes per triangle, up to 128 triangles and 16 KiB. Finite little-endian float32 values and zero attribute counts only; header remains opaque. ASCII STL, color extensions and mesh repair excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [github.com](https://github.com/mrdoob/three.js/blob/dev/examples/jsm/loaders/STLLoader.js). No endorsement is implied.

Example input:

```json
{
  "hex": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000803f0000000000000000000000000000803f0000000000000000000000000000803f000000000000"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/triangleCount": 1,
  "/triangles": [
    [
      [
        0,
        0,
        0
      ],
      [
        1,
        0,
        0
      ],
      [
        0,
        1,
        0
      ]
    ]
  ],
  "/normals": [
    [
      0,
      0,
      1
    ]
  ]
}
```

## ELF64 Section Profile API

USD 3.00 per job.

Inspect ELF64 little-endian section declarations and names. Up to 16 KiB of ELF64 little-endian version 1 bytes; 64-byte headers and section entries, with 1–64 sections. Bounds-check stored sections and optional ASCII names; NOBITS sizes remain exact metadata. Extended numbering, loading, relocation and executable safety assessment excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [gabi.xinuos.com](https://gabi.xinuos.com/elf/03-sheader.html). No endorsement is implied.

Example input:

```json
{
  "hex": "7f454c4602010100000000000000000001003e00010000000000000000000000000000000000000040000000000000000000000040000000000040000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/machine": 62,
  "/sectionCount": 1,
  "/sections/0/type": 0
}
```

## USTAR Archive Directory API

USD 3.00 per job.

Read member metadata from a bounded POSIX USTAR archive. Up to 16 KiB and 64 USTAR members, aligned to 512 bytes with two terminal zero blocks. Validate ASCII names, octal fields and checksums. Regular files and directories only; no extraction, links, PAX, GNU or sparse extensions. Names remain metadata. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.gnu.org](https://www.gnu.org/software/tar/manual/html_node/Standard.html). No endorsement is implied.

Example input:

```json
{
  "hex": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/entries": [],
  "/entryCount": 0
}
```

## Classic PCAP Packet Index API

USD 3.00 per job.

Index captured packet records with exact timestamps and size checks. Classic PCAP 2.4 in either byte order, with microsecond or nanosecond timestamps. Up to 128 records and 16 KiB; reserved global fields zero, snapshot length 1–65535. Validate captured lengths and preserve exact timestamp integers. PCAPNG and packet-payload decoding excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [github.com](https://github.com/the-tcpdump-group/libpcap/blob/master/pcap-savefile.manfile.in). No endorsement is implied.

Example input:

```json
{
  "hex": "d4c3b2a1020004000000000000000000ffff000001000000"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/packetCount": 0,
  "/snapLength": 65535,
  "/linkType": 1,
  "/timestampUnit": "microseconds"
}
```

## Netpbm Plain Raster Codec API

USD 3.00 per job.

Decode or emit plain PBM,PGM and PPM sample arrays. One plain ASCII P1, P2 or P3 image, dimensions 1–64 and at most 4096 samples. P1 accepts compact binary pixels; P2/P3 use decimal samples with maxval 1–65535. Comments allowed; canonical text is at most 24591 characters. Trailing data excluded. Decode requires image=null; encode requires empty text. Binary formats and color conversion excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [netpbm.sourceforge.net](https://netpbm.sourceforge.net/doc/pnm.html). No endorsement is implied.

Example input:

```json
{
  "mode": "decode",
  "text": "P1\n2 1\n0 1\n",
  "image": null
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/image/format": "P1",
  "/image/width": 2,
  "/image/samples": [
    0,
    1
  ]
}
```

## DNS Message Wire Inspector API

USD 3.00 per job.

Decode bounded DNS questions and resource records including compressed names. Up to 4 KiB, 16 questions and 64 resource records. Validate backward compression pointers and 255-byte names with restricted ASCII labels. Decode selected A, AAAA, name, TXT and MX records; retain unknown RDATA as hex. No DNS queries, DNSSEC or resolver qualification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc1035). No endorsement is implied.

Example input:

```json
{
  "hex": "12340100000100000000000001780000010001"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/id": 4660,
  "/questions/0/name": "x",
  "/questions/0/type": 1,
  "/records": []
}
```

## DHCPv4 Message Option Inspector API

USD 3.00 per job.

Parse BOOTP fixed fields and the DHCPv4 option sequence. Up to 4 KiB; Ethernet address length six, DHCP cookie and one message-type option required. Validate option lengths, padding and end marker; reject option overload and nonzero trailing bytes. No DHCP exchange or lease verification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc2131). No endorsement is implied.

Example input:

```json
{
  "hex": "010106000000123400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000063825363350101ff"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/transactionId": 4660,
  "/messageType": 1,
  "/hardwareAddress": "000000000000"
}
```

## NTPv4 Packet Inspector API

USD 3.00 per job.

Inspect one fixed NTPv4 packet with exact timestamp ticks. Exactly 48 bytes, NTP version 4, modes 1–7 and stratum 0–16. Decode signed fields and fixed-point values; preserve four 64-bit timestamps as exact tick strings. Era inference, extensions, MAC verification and clock synchronization excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc5905). No endorsement is implied.

Example input:

```json
{
  "hex": "230206ec0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/version": 4,
  "/mode": 3,
  "/stratum": 2,
  "/precision": -20,
  "/transmitTicks": "0"
}
```

## RTP Packet Inspector API

USD 3.00 per job.

Separate an RTPv2 header,CSRCs,extension,padding and opaque payload. RTP version 2 packet up to 16 KiB, with 0–15 CSRC entries, optional word-counted extension and validated padding. Payload remains opaque. No SRTP decryption, codec decoding or session-continuity validation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc3550). No endorsement is implied.

Example input:

```json
{
  "hex": "8060002a0000005a00000001aabb"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/payloadType": 96,
  "/sequence": 42,
  "/timestamp": 90,
  "/payloadHex": "aabb"
}
```

## RTCP Compound Framing API

USD 3.00 per job.

Index RTCPv2 packets and reconcile length,padding and report-block counts. Up to 16 KiB and 64 RTCP packets of types 200–204. Validate sender/receiver report lengths and 24-byte report blocks; other bodies remain raw. Padding allowed only on the final packet. CNAME, session semantics and SRTCP authentication excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc3550). No endorsement is implied.

Example input:

```json
{
  "hex": "80c9000100000001"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/packetCount": 1,
  "/packets/0/type": 201,
  "/packets/0/reportCount": 0
}
```

## CoAP Message Inspector API

USD 3.00 per job.

Decode CoAPv1 tokens,delta-encoded options and payload framing. CoAP version 1 datagram up to 16 KiB, token length 0–8 and at most 128 options. Validate extended option deltas and lengths, payload markers and empty-message framing. Unknown values remain raw; no requests, DTLS or block reassembly. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc7252). No endorsement is implied.

Example input:

```json
{
  "hex": "40011234b178ff01"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/messageId": 4660,
  "/code": "0.01",
  "/options/0/number": 11,
  "/payloadHex": "01"
}
```

## MPEG Transport Packet Inspector API

USD 3.00 per job.

Inspect a188byte MPEG transport packet and optional PCR clock. Exactly 188 bytes with sync byte 0x47 and valid adaptation framing. Decode the optional 33-bit PCR base and 9-bit extension into exact ticks; other adaptation fields and payload remain opaque. No FEC, PES/PSI assembly or broadcast qualification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.itu.int](https://www.itu.int/rec/T-REC-H.222.0). No endorsement is implied.

Example input:

```json
{
  "hex": "47410010ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/pid": 256,
  "/payloadUnitStart": true,
  "/payloadBytes": 184,
  "/pcrTicks": null
}
```

## IPv4 Packet Header Inspector API

USD 3.00 per job.

Decode an IPv4 header and options and calculate its checksum status. Complete IPv4 packet up to 16 KiB with exact total length, 20–60-byte header and zero reserved flag. Validate option framing and report checksum validity and fragment metadata. Payload remains opaque; no transport or session verification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc791). No endorsement is implied.

Example input:

```json
{
  "hex": "450000140001000040118ea1c0000201c6336402"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/source": "192.0.2.1",
  "/destination": "198.51.100.2",
  "/headerBytes": 20,
  "/checksumValid": true
}
```

## IPv6 Extension Chain Inspector API

USD 3.00 per job.

Walk bounded IPv6 extension headers and retain the terminal payload. Complete IPv6 packet up to 16 KiB, no jumbograms. Walk at most 16 supported extension headers and one Fragment header. Continue after an atomic fragment; stop at genuinely fragmented data, ESP or an unknown type and retain opaque bytes. No reassembly, decryption or transport validation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc8200). No endorsement is implied.

Example input:

```json
{
  "hex": "6000000000003b400000000000000000000000000000000100000000000000000000000000000002"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/terminalHeader": 59,
  "/source": "0000:0000:0000:0000:0000:0000:0000:0001",
  "/extensions": []
}
```

## TCP Segment Option Inspector API

USD 3.00 per job.

Decode a TCP header and structurally validate its option list. Supplied TCP segment up to 16 KiB with 20–60-byte header and zero reserved bits. Validate option framing and lengths for MSS, window scale, SACK and timestamps. Payload remains opaque; no checksum assertion without a pseudoheader or connection verification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [datatracker.ietf.org](https://datatracker.ietf.org/doc/html/rfc9293). No endorsement is implied.

Example input:

```json
{
  "hex": "303901bb00000001000000005002100000000000"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/sourcePort": 12345,
  "/destinationPort": 443,
  "/sequence": 1,
  "/flags": 2,
  "/options": []
}
```

## Bounded Raw DEFLATE Decoder API

USD 3.00 per job.

Decode raw DEFLATE blocks under an enforced output ceiling. Raw RFC 1951 stored, fixed and dynamic Huffman blocks; up to 4 KiB compressed, 256 blocks and 16384 output bytes. Enforce outputLimit during every expansion and reject invalid trees, distances, truncation and trailing bytes. Gzip/zlib envelopes and compression excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.rfc-editor.org](https://www.rfc-editor.org/rfc/rfc1951). No endorsement is implied.

Example input:

```json
{
  "hex": "010200fdff4869",
  "outputLimit": 16
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/hex": "4869",
  "/byteLength": 2
}
```

## LZ4 Raw Block Decoder API

USD 3.00 per job.

Decode raw LZ4 literal and match sequences with bounded expansion. Raw LZ4 blocks up to 4 KiB compressed and 16384 output bytes. Validate offsets and lengths while enforcing outputLimit during expansion; require a final literal-only sequence. Frames, dictionaries, checksums and compressor-optimization rules excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [github.com](https://github.com/lz4/lz4/blob/dev/doc/lz4_Block_format.md). No endorsement is implied.

Example input:

```json
{
  "hex": "30414243",
  "outputLimit": 16
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/hex": "414243",
  "/byteLength": 3
}
```

## Snappy Raw Block Decoder API

USD 3.00 per job.

Decode Snappy raw literals and three copy-tag forms. Raw Snappy blocks up to 4 KiB compressed and 16384 declared output bytes. Validate the 32-bit length prefix, all copy forms and exact decoded length while enforcing outputLimit during expansion. Framed checksums and dictionaries excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [github.com](https://github.com/google/snappy/blob/main/format_description.txt). No endorsement is implied.

Example input:

```json
{
  "hex": "0308414243",
  "outputLimit": 16
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/hex": "414243",
  "/byteLength": 3
}
```

## LZW Dictionary Codec API

USD 3.00 per job.

Encode bytes to LZW integer codes or reconstruct the bytes. Initial byte dictionary 0–255 and learned codes 256–4095, with no reset, end codes or bit packing. Up to 4096 input/output bytes and codes, with bounded dictionary storage. Encode requires codes=[]; decode requires empty hex. No GIF, TIFF or Unix compress compatibility claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cmu.edu](https://www.cs.cmu.edu/~guyb/realworld/compression.pdf). No endorsement is implied.

Example input:

```json
{
  "mode": "encode",
  "hex": "41424142414241",
  "codes": []
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/codes": [
    65,
    66,
    256,
    258
  ]
}
```

## LZ78 Phrase Token Codec API

USD 3.00 per job.

Encode bytes as dictionary-index/literal tokens and decode them. Dictionary index zero means empty; learned phrases use positive indices. A null literal may end only the final existing phrase. Up to 4096 bytes, 1024 tokens and 64 KiB of dictionary storage; reject encoding that would exceed the token ceiling. Encode requires tokens=[]; decode requires empty hex. Explicit token format only. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cmu.edu](https://www.cs.cmu.edu/~guyb/realworld/compression.pdf). No endorsement is implied.

Example input:

```json
{
  "mode": "encode",
  "hex": "41424142414241",
  "tokens": []
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/tokens": [
    {
      "index": 0,
      "byte": 65
    },
    {
      "index": 0,
      "byte": 66
    },
    {
      "index": 1,
      "byte": 66
    },
    {
      "index": 3,
      "byte": 65
    }
  ]
}
```

## COBS Frame Codec API

USD 3.00 per job.

Encode arbitrary bytes as a zero-free COBS frame or decode it. COBS frame payload only, excluding the zero delimiter. Up to 4096 payload bytes and 4114 encoded bytes. Reject zero codes, truncated blocks and oversized decoded output. No CRC, transport or delivery verification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.stuartcheshire.org](https://www.stuartcheshire.org/papers/COBSforToN.pdf). No endorsement is implied.

Example input:

```json
{
  "mode": "encode",
  "hex": "1100220033"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/hex": "021102220233"
}
```

## Hamming SECDED Codec API

USD 3.00 per job.

Encode even-parity extended Hamming words or diagnose single/double errors. 1–64 data bits with even-parity positions 1, 2, 4 and so on, followed by overall even parity. Correct a single-bit error and flag double-bit errors; no guarantee for three or more errors. Mode determines the required bit length. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/). No endorsement is implied.

Example input:

```json
{
  "mode": "encode",
  "dataBits": 4,
  "bits": "1011"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/codeword": "01100110",
  "/data": "1011",
  "/uncorrectable": false
}
```

## Reed Solomon Erasure Recovery API

USD 3.00 per job.

Recover polynomial coefficient shards and requested evaluations from intact shards. GF(256) polynomial coefficients under modulus 0x11d; k=1–16, distinct evaluation points 0–255, up to 32 known and requested shards of 128 bytes each. Require at least k intact equal-length shards and verify extras. Erasures only; no corruption correction or packet-format compatibility claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/coding/sage/coding/grs_code.html). No endorsement is implied.

Example input:

```json
{
  "dataShards": 2,
  "samples": [
    {
      "point": 0,
      "hex": "01"
    },
    {
      "point": 1,
      "hex": "03"
    }
  ],
  "recoverPoints": [
    2
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coefficients": [
    "01",
    "02"
  ],
  "/recovered/0/hex": "05"
}
```

## Convolutional Viterbi Decoder API

USD 3.00 per job.

Decode hard-decision bits for a fixed rate-one-half convolutional code. Fixed rate-one-half code, constraint length three, octal generators 7 and 5, newest bit in the low register position and initial state zero. Decode 1–256 hard-decision symbols with any or zero final state; lexicographic bit-string ties. Soft decisions and puncturing excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/6-02-introduction-to-eecs-ii-digital-communication-systems-fall-2012/). No endorsement is implied.

Example input:

```json
{
  "received": "111011",
  "finalState": "zero"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/decoded": "100",
  "/distance": 0,
  "/stateTrace": [
    0,
    1,
    2,
    0
  ]
}
```

## Exact Arithmetic Interval Codec API

USD 3.00 per job.

Encode token messages as exact rational intervals and decode a rational tag. 1–16 ordered symbols with positive integer frequencies and at most 128 tokens. Exact reduced rational intervals and midpoint tags. Decode requires tokens=[] and a tag in [0,1); encode requires tag=null and matching length. Ideal arithmetic intervals only, with no streaming bit-format claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cmu.edu](https://www.cs.cmu.edu/~guyb/realworld/compression.pdf). No endorsement is implied.

Example input:

```json
{
  "mode": "encode",
  "model": [
    {
      "symbol": "A",
      "frequency": 1
    },
    {
      "symbol": "B",
      "frequency": 1
    }
  ],
  "tokens": [
    "A",
    "B"
  ],
  "tag": null,
  "length": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/lower": {
    "n": "1",
    "d": "4"
  },
  "/upper": {
    "n": "1",
    "d": "2"
  },
  "/tag": {
    "n": "3",
    "d": "8"
  }
}
```

## Minimum Cost Bounded Flow API

USD 3.00 per job.

Find a minimum-cost integral flow for a requested quantity. Up to 16 vertices, 64 directed edges, capacities and requested flow up to 1024; nonnegative integer edge costs. Residual shortest paths return the maximum deliverable quantity up to the request and its exact decimal-string cost. Parallel edges allowed; self-loops excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [networkx.org](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.flow.min_cost_flow.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "source": 0,
  "sink": 2,
  "quantity": 2,
  "edges": [
    {
      "from": 0,
      "to": 1,
      "capacity": 2,
      "cost": 1
    },
    {
      "from": 1,
      "to": 2,
      "capacity": 2,
      "cost": 2
    },
    {
      "from": 0,
      "to": 2,
      "capacity": 1,
      "cost": 9
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/flow": 2,
  "/cost": "6",
  "/edgeFlows": [
    2,
    2,
    0
  ]
}
```

## Exact Maximum Clique API

USD 3.00 per job.

Find the largest complete vertex subset of a small graph. Simple undirected graphs with 1–20 vertices. Exact branch and bound; lexicographically smallest sorted witness among ties. At most two million search states; exceeding the bound rejects the request. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [networkx.org](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.clique.find_cliques.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 4,
  "edges": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 1,
      "to": 2
    },
    {
      "from": 0,
      "to": 2
    },
    {
      "from": 2,
      "to": 3
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/size": 3,
  "/clique": [
    0,
    1,
    2
  ]
}
```

## Exact Graph Chromatic Number API

USD 3.00 per job.

Find the minimum number of colors and a proper vertex coloring. Simple undirected graphs with 1–12 vertices. Exact saturation-order search with deterministic ties and at most two million search states; no heuristic optimum claim or fixed color-label convention. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_coloring.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "edges": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 1,
      "to": 2
    },
    {
      "from": 0,
      "to": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/chromaticNumber": 3
}
```

## Graph Isomorphism Witness API

USD 3.00 per job.

Compare small graphs and return a vertex relabeling when they are isomorphic. Two simple undirected graphs on the same 1–12 vertices. Degree-pruned exact search; the first ascending mapping is returned. At most two million search states; labels, weights and multigraphs excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [networkx.org](https://networkx.org/documentation/stable/reference/algorithms/isomorphism.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "left": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 1,
      "to": 2
    }
  ],
  "right": [
    {
      "from": 0,
      "to": 2
    },
    {
      "from": 2,
      "to": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/isomorphic": true,
  "/mapping": [
    0,
    2,
    1
  ]
}
```

## Directed Simple Cycle Enumeration API

USD 3.00 per job.

Enumerate distinct simple cycles of a directed graph. Up to 12 vertices and 36 edges, no duplicate edges or self-loops. Cycles start at their smallest vertex without repeating the closing vertex; reverse directions remain distinct. At most 256 cycles and two million search states; larger results reject. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [networkx.org](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.cycles.simple_cycles.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "edges": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 1,
      "to": 2
    },
    {
      "from": 2,
      "to": 0
    },
    {
      "from": 1,
      "to": 0
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/cycles": [
    [
      0,
      1
    ],
    [
      0,
      1,
      2
    ]
  ],
  "/count": 2
}
```

## Undirected Chinese Postman Route API

USD 3.00 per job.

Find a shortest closed walk covering every supplied edge. Connected simple undirected graphs with 1–12 vertices and positive integer edge weights. Exact shortest paths and odd-vertex pairing; return vertex and input-edge walks plus exact cost. Isolated singleton allowed; no directed streets or turn restrictions. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.mit.edu](https://web.mit.edu/urban_or_book/www/book/chapter6/6.4.4.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "start": 0,
  "edges": [
    {
      "from": 0,
      "to": 1,
      "weight": 2
    },
    {
      "from": 1,
      "to": 2,
      "weight": 3
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/cost": "10",
  "/edgeMultiplicity": [
    2,
    2
  ]
}
```

## Minimum Mean Directed Cycle API

USD 3.00 per job.

Find a directed cycle with the smallest exact average edge weight. Simple directed graphs with up to 8 vertices and integer weights. Exhaustive canonical simple-cycle search returns a reduced rational mean and witness; null when acyclic. Self-loops excluded; bounded by the complete 8-vertex graph. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.sciencedirect.com](https://www.sciencedirect.com/science/article/pii/0012365X78900110). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "edges": [
    {
      "from": 0,
      "to": 1,
      "weight": 1
    },
    {
      "from": 1,
      "to": 0,
      "weight": 2
    },
    {
      "from": 1,
      "to": 2,
      "weight": 0
    },
    {
      "from": 2,
      "to": 1,
      "weight": 0
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/mean": {
    "n": "0",
    "d": "1"
  },
  "/cycle": [
    1,
    2
  ]
}
```

## Graph Betweenness Centrality API

USD 3.00 per job.

Measure each vertex share of shortest paths between other vertices. Unweighted simple graphs with 1–32 vertices; directed or undirected. Exact shortest-path counts with approximate ratios, endpoint-excluding raw and normalized scores; disconnected pairs contribute zero. No weighted or sampled approximation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [networkx.org](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.centrality.betweenness_centrality.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "directed": false,
  "edges": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 1,
      "to": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/raw": [
    0,
    1,
    0
  ],
  "/normalized": [
    0,
    1,
    0
  ]
}
```

## Graph Core Decomposition API

USD 3.00 per job.

Compute every vertex core number and graph degeneracy. Simple undirected graphs with 1–64 vertices and up to 512 edges. Degree peeling returns maximal k-core membership numbers, including zero for isolated vertices; no directed or weighted-core interpretation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [networkx.org](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.core.core_number.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 4,
  "edges": [
    {
      "from": 0,
      "to": 1
    },
    {
      "from": 1,
      "to": 2
    },
    {
      "from": 0,
      "to": 2
    },
    {
      "from": 2,
      "to": 3
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coreNumbers": [
    2,
    2,
    2,
    1
  ],
  "/degeneracy": 2
}
```

## Minimum Directed Arborescence API

USD 3.00 per job.

Find a minimum-cost directed spanning tree reaching outward from a chosen root. Up to 12 vertices and 64 distinct directed edges with integer costs. Exact vertex-subset dynamic programming; return input-edge indices and exact decimal-string cost, or infeasible when no rooted spanning tree exists. Self-loops excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [networkx.org](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.tree.branchings.minimum_spanning_arborescence.html). No endorsement is implied.

Example input:

```json
{
  "vertices": 3,
  "root": 0,
  "edges": [
    {
      "from": 0,
      "to": 1,
      "weight": 4
    },
    {
      "from": 0,
      "to": 2,
      "weight": 8
    },
    {
      "from": 1,
      "to": 2,
      "weight": 1
    },
    {
      "from": 2,
      "to": 1,
      "weight": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/feasible": true,
  "/cost": "5",
  "/edges": [
    0,
    2
  ]
}
```

## Integer Smith Normal Form API

USD 3.00 per job.

Compute the invariant factors and Smith diagonal of an integer matrix. Rectangular matrices up to 5 by 5 with entries within one million. Exact determinantal-divisor computation; nonnegative diagonal with successive divisibility, zeros last. Transformation matrices are excluded. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/matrices/sage/matrix/matrix_integer_dense.html). No endorsement is implied.

Example input:

```json
{
  "matrix": [
    [
      2,
      4
    ],
    [
      6,
      8
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/invariantFactors": [
    "2",
    "4"
  ],
  "/diagonal": [
    [
      "2",
      "0"
    ],
    [
      "0",
      "4"
    ]
  ],
  "/rank": 2
}
```

## Integer Row Hermite Normal Form API

USD 3.00 per job.

Canonicalize the integer row lattice of a matrix. Matrices up to 5 by 5 with entries within one million. Row echelon convention: positive pivots, entries above each pivot reduced into its half-open residue range, zero rows last. Exact integer row operations; 512-bit intermediate and 100000-operation ceilings. No column-lattice convention or transformation matrix. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/matrices/sage/matrix/matrix_integer_dense.html). No endorsement is implied.

Example input:

```json
{
  "matrix": [
    [
      2,
      4
    ],
    [
      6,
      8
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/matrix": [
    [
      "2",
      "0"
    ],
    [
      "0",
      "4"
    ]
  ],
  "/rank": 2
}
```

## Rational Polynomial Bezout API

USD 3.00 per job.

Find a monic polynomial gcd and exact Bezout coefficient polynomials. Ascending integer coefficient arrays, degrees up to 8 and coefficient magnitude up to one million. Exact rational Euclidean arithmetic with a 4096-bit intermediate ceiling; both zero polynomials rejected. Trailing zero coefficients must be omitted. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/polynomial_rational_flint.html). No endorsement is implied.

Example input:

```json
{
  "a": [
    "-1",
    "0",
    "1"
  ],
  "b": [
    "-1",
    "1"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/gcd": [
    {
      "n": "-1",
      "d": "1"
    },
    {
      "n": "1",
      "d": "1"
    }
  ],
  "/s": [
    {
      "n": "0",
      "d": "1"
    }
  ],
  "/t": [
    {
      "n": "1",
      "d": "1"
    }
  ]
}
```

## Sturm Real Root Isolation API

USD 3.00 per job.

Isolate distinct real polynomial roots inside a supplied interval. Nonzero integer polynomials of degree 1–8, ascending coefficients within one million. Integer interval bounds within one million must not be roots. Exact square-free Sturm arithmetic gives dyadic intervals of width at most 2 to the negative precisionBits, or exact dyadic roots. Multiplicities excluded; 4096-bit arithmetic, 4096 nodes and 64 subdivision levels. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.sympy.org](https://docs.sympy.org/latest/modules/polys/reference.html#sympy.polys.polytools.sturm). No endorsement is implied.

Example input:

```json
{
  "coefficients": [
    "-2",
    "0",
    "1"
  ],
  "lower": 0,
  "upper": 2,
  "precisionBits": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/rootCount": 1,
  "/intervals/0/lower": {
    "n": "5",
    "d": "4"
  },
  "/intervals/0/upper": {
    "n": "3",
    "d": "2"
  }
}
```

## Exact Polynomial Resultant API

USD 3.00 per job.

Compute a polynomial pair resultant and the first polynomial discriminant. Ascending integer coefficients within one million, degrees 1–8 with nonzero leading terms. Exact Sylvester determinants and decimal-string results. No symbolic parameters, multivariate polynomials or numerical root approximation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/polynomial_rational_flint.html). No endorsement is implied.

Example input:

```json
{
  "a": [
    "-2",
    "0",
    "1"
  ],
  "b": [
    "-1",
    "1"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/resultant": "-1",
  "/discriminant": "8"
}
```

## Exact Continued Fraction Convergents API

USD 3.00 per job.

Expand a rational number and return all regular continued-fraction convergents. Signed decimal-string numerator and positive denominator, up to 30 digits each. Floor-based regular continued fractions work for negative values; reduced exact convergents and canonical final partial quotient. No irrational or floating-point guessing. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [dlmf.nist.gov](https://dlmf.nist.gov/1.12). No endorsement is implied.

Example input:

```json
{
  "numerator": "355",
  "denominator": "113"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/partialQuotients": [
    "3",
    "7",
    "16"
  ],
  "/convergents/2": {
    "n": "355",
    "d": "113"
  }
}
```

## Pell Fundamental Solution API

USD 3.00 per job.

Find the least positive solution of x squared minus D times y squared equals one. Nonsquare integer D from 2 through 10000. Exact continued-fraction convergents; return positive fundamental x and y as decimal strings. Squares rejected; at most 10000 convergents and 4096-bit results. No generalized Pell equation or negative-one solution claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.sympy.org](https://docs.sympy.org/latest/modules/solvers/diophantine.html#sympy.solvers.diophantine.diophantine.diop_DN). No endorsement is implied.

Example input:

```json
{
  "D": 13
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/x": "649",
  "/y": "180"
}
```

## Exact Linear Recurrence Term API

USD 3.00 per job.

Evaluate a distant term of a supplied constant-coefficient recurrence. Order 1–8, signed integer coefficients and initial values with at most 12 digits; index 0–1000000. Companion-matrix powering returns an exact decimal string. Operations reject intermediates beyond 8192 bits rather than approximate an oversized result. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/matrices/sage/matrix/berlekamp_massey.html). No endorsement is implied.

Example input:

```json
{
  "coefficients": [
    "1",
    "1"
  ],
  "initial": [
    "0",
    "1"
  ],
  "index": 10
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/value": "55"
}
```

## Cyclic Necklace Orbit Count API

USD 3.00 per job.

Count color strings up to rotation and primitive rotational orbits. Length 1–512 and 1–256 labeled colors. Exact Burnside and Möbius sums returned as decimal strings; rotations identified, reflections remain distinct. No representative generation or fixed-content constraint. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/necklace.html). No endorsement is implied.

Example input:

```json
{
  "length": 4,
  "colors": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/necklaces": "6",
  "/primitiveNecklaces": "3"
}
```

## Rook Polynomial Board Count API

USD 3.00 per job.

Count nonattacking rook placements of every possible size on a supplied board. Rectangular boolean boards up to 12 by 12; true marks an allowed square. Exact row and occupied-column dynamic programming; coefficients count indistinguishable nonattacking rooks, including the empty placement. No chess move simulation or weighted placements. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.sagemath.org](https://doc.sagemath.org/html/en/reference/matrices/sage/matrix/matrix2.html#sage.matrix.matrix2.Matrix.rook_vector). No endorsement is implied.

Example input:

```json
{
  "board": [
    [
      true,
      true
    ],
    [
      true,
      true
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coefficients": [
    "1",
    "4",
    "2"
  ],
  "/maximumRooks": 2
}
```

## Binary Grid Morphology API

USD 3.00 per job.

Apply erosion, dilation, opening or closing to a supplied binary grid. Up to 64 × 64 cells with a nonempty odd-sized kernel up to 7 × 7. Centered anchor, reflected kernel for dilation and constant-zero padding at each stage; boundary behavior is explicit. No image-file decoding. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.opencv.org](https://docs.opencv.org/4.13.0/d4/d86/group__imgproc__filter.html). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      0,
      0,
      0
    ],
    [
      0,
      1,
      0
    ],
    [
      0,
      0,
      0
    ]
  ],
  "kernel": [
    [
      1,
      1,
      1
    ]
  ],
  "operation": "dilate"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/grid": [
    [
      0,
      0,
      0
    ],
    [
      1,
      1,
      1
    ],
    [
      0,
      0,
      0
    ]
  ],
  "/foregroundCount": 3
}
```

## Squared Euclidean Grid Distance API

USD 3.00 per job.

Find the exact squared pixel distance to an in-grid background cell. Up to 32 × 32 binary cells with at least one zero. Unit row/column spacing; squared integer distances and nearest-zero coordinates, with row-major ties. No implicit background outside the grid or physical-distance inference. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.distance_transform_edt.html). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      0,
      1,
      1
    ],
    [
      1,
      1,
      1
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/squaredDistance": [
    [
      0,
      1,
      4
    ],
    [
      1,
      2,
      5
    ]
  ],
  "/nearestZero/1/2": {
    "row": 0,
    "column": 0
  }
}
```

## Marching Squares Contour Segments API

USD 3.00 per job.

Extract linearly interpolated contour segments from a supplied scalar grid. Up to 32 × 32 cells. Level values equal to a grid vertex are rejected to avoid degenerate segments. Low-valued diagonals are connected in saddle cells; output is a deterministic segment list, not stitched polygons or a surface model. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [scikit-image.org](https://scikit-image.org/docs/stable/api/skimage.measure.html#skimage.measure.find_contours). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      1,
      0
    ],
    [
      0,
      0
    ]
  ],
  "level": 0.5
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/segments": [
    {
      "from": {
        "x": 0,
        "y": 0.5
      },
      "to": {
        "x": 0.5,
        "y": 0
      }
    }
  ],
  "/segmentCount": 1
}
```

## Zhang–Suen Binary Thinning API

USD 3.00 per job.

Apply the two-pass Zhang–Suen deletion rules to a binary grid. Up to 32 × 32 cells with zero-valued exterior padding. Simultaneous deletion within each pass continues to a fixed point. Reports removed cells and full iterations including the final unchanged iteration; no topology-preservation guarantee or image-file processing. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [scikit-image.org](https://scikit-image.org/docs/stable/api/skimage.morphology.html#skimage.morphology.skeletonize). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      0,
      0,
      0
    ],
    [
      1,
      1,
      1
    ],
    [
      0,
      0,
      0
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/grid": [
    [
      0,
      0,
      0
    ],
    [
      1,
      1,
      1
    ],
    [
      0,
      0,
      0
    ]
  ],
  "/removed": 0,
  "/iterations": 1
}
```

## Minimum Energy Vertical Seam API

USD 3.00 per job.

Find a minimum-total-energy top-to-bottom raster seam. Up to 64 × 64 supplied nonnegative energy values. Each step moves at most one column; ties use the lexicographically smallest complete column path. Does not infer image energy, resize a file or remove pixels. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.merl.com](https://www.merl.com/publications/TR2007-087). No endorsement is implied.

Example input:

```json
{
  "energy": [
    [
      1,
      9,
      9
    ],
    [
      9,
      1,
      9
    ],
    [
      9,
      9,
      1
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/columns": [
    0,
    1,
    2
  ],
  "/totalEnergy": 3
}
```

## Bilinear Raster Warp API

USD 3.00 per job.

Resample a scalar grid using a supplied inverse affine mapping. Input and output up to 64 × 64. Coefficients map output pixel centers (x, y) to source coordinates; bilinear interpolation uses edge-clamped neighbors inside the source domain and the supplied fill for coordinates outside it. No coordinate-reference-system or antialiasing inference. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.opencv.org](https://docs.opencv.org/4.13.0/da/d54/group__imgproc__transform.html). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      0,
      10
    ],
    [
      20,
      30
    ]
  ],
  "inverseAffine": [
    0,
    0,
    0.5,
    0,
    0,
    0.5
  ],
  "width": 1,
  "height": 1,
  "fill": -1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/grid": [
    [
      15
    ]
  ],
  "/outsideSamples": 0
}
```

## Binary Region Quadtree Codec API

USD 3.00 per job.

Encode or decode a bounded square binary region quadtree. Power-of-two sizes from 1 to 32. Prefix format uses 0/1 leaves and X followed by top-left, top-right, bottom-left, bottom-right children. Encoding requires an empty code; decoding requires grid [[0]] as the unused-field placeholder. No archive access or compression-ratio promise. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [donar.umiacs.umd.edu](https://donar.umiacs.umd.edu/quadtree/regions/regionquad.html). No endorsement is implied.

Example input:

```json
{
  "mode": "encode",
  "size": 2,
  "grid": [
    [
      0,
      1
    ],
    [
      1,
      0
    ]
  ],
  "code": ""
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/code": "X0110",
  "/leafCount": 4,
  "/nodeCount": 5
}
```

## Gray Co-occurrence Texture API

USD 3.00 per job.

Calculate a gray-level pair histogram and descriptive texture measures. Up to 64 × 64 supplied quantized cells with 2–16 levels. One nonzero row/column offset from −7 to 7, optional symmetric counting, and at least one in-bounds pair. Returns contrast, dissimilarity, homogeneity, energy and base-two entropy; no image classification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [scikit-image.org](https://scikit-image.org/docs/stable/api/skimage.feature.html#skimage.feature.graycomatrix). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      0,
      1
    ],
    [
      1,
      0
    ]
  ],
  "levels": 2,
  "rowOffset": 0,
  "columnOffset": 1,
  "symmetric": false
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/counts": [
    [
      0,
      1
    ],
    [
      1,
      0
    ]
  ],
  "/pairCount": 2,
  "/contrast": 1,
  "/dissimilarity": 1,
  "/homogeneity": 0.5,
  "/angularSecondMoment": 0.5,
  "/entropy": 1
}
```

## Grayscale Histogram Equalization API

USD 3.00 per job.

Equalize an eight-bit grayscale grid with an inspectable lookup table. Up to 64 × 64 cells. Uses the cumulative histogram after subtracting the first occupied count, scales to 0–255 and rounds half up. Constant-valued input remains unchanged. Returns original histogram and lookup; no image-file or color-space handling. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.opencv.org](https://docs.opencv.org/4.13.0/d6/dc7/group__imgproc__hist.html). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      0,
      0
    ],
    [
      128,
      255
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/grid": [
    [
      0,
      0
    ],
    [
      128,
      255
    ]
  ],
  "/lookup/128": 128
}
```

## Otsu Binary Threshold API

USD 3.00 per job.

Select a global eight-bit threshold by maximum between-class variance. Up to 64 × 64 cells. Exact integer-ratio comparisons select the lowest threshold on a tie; foreground means pixel greater than threshold. A constant image returns threshold zero with variance zero. No local/adaptive thresholding or semantic image assessment. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.opencv.org](https://docs.opencv.org/4.13.0/d7/d1b/group__imgproc__misc.html). No endorsement is implied.

Example input:

```json
{
  "grid": [
    [
      0,
      0
    ],
    [
      255,
      255
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/threshold": 0,
  "/grid": [
    [
      0,
      0
    ],
    [
      1,
      1
    ]
  ],
  "/betweenClassVariance": 16256.25
}
```

## Bounded Voronoi Cells API

USD 3.00 per job.

Partition a rectangle into nearest-site Euclidean cells. Up to 32 distinct integer sites and an integer rectangle, coordinates within one million. Exact rational half-plane clipping; return approximate vertices and exact rational cell areas, including empty cells for outside sites. Unweighted planar distances only. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Voronoi_diagram_2/index.html). No endorsement is implied.

Example input:

```json
{
  "sites": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    }
  ],
  "bounds": {
    "minX": -1,
    "minY": -1,
    "maxX": 3,
    "maxY": 1
  }
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/cells/0/area": {
    "n": "4",
    "d": "1"
  },
  "/cells/1/area": {
    "n": "4",
    "d": "1"
  }
}
```

## Delaunay Triangulation API

USD 3.00 per job.

Triangulate a small planar point set using the empty-circle criterion. 3–24 distinct integer points within one million. Exact orientation and incircle predicates; reject any collinear triple or cocircular quadruple. Counterclockwise triangles reference input indices; no constraint edges, perturbation or degenerate-site convention. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Triangulation_2/index.html). No endorsement is implied.

Example input:

```json
{
  "points": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    },
    {
      "x": 0,
      "y": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/triangles": [
    [
      0,
      1,
      2
    ]
  ]
}
```

## Simple Polygon Ear Triangulation API

USD 3.00 per job.

Split a simple polygon into nonoverlapping triangles. 3–64 distinct integer vertices in boundary order, within one million; either winding accepted. Reject crossings, touching nonadjacent edges and consecutive collinear vertices. Exact predicates and area; triangles retain input indices. No holes or inserted vertices. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Partition_2/index.html). No endorsement is implied.

Example input:

```json
{
  "polygon": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    },
    {
      "x": 2,
      "y": 2
    },
    {
      "x": 0,
      "y": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/area": {
    "n": "4",
    "d": "1"
  },
  "/triangles": [
    [
      3,
      0,
      1
    ],
    [
      1,
      2,
      3
    ]
  ]
}
```

## Convex Polygon Minkowski Sum API

USD 3.00 per job.

Compute the convex polygon of all pairwise vector sums. Two strictly convex counterclockwise integer polygons, 3–32 vertices each, within one million. Exact pair sums and monotone convex hull remove collinear boundary points. No nonconvex decomposition, holes or offset-circle approximation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Minkowski_sum_2/index.html). No endorsement is implied.

Example input:

```json
{
  "a": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 1,
      "y": 0
    },
    {
      "x": 0,
      "y": 1
    }
  ],
  "b": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 1,
      "y": 0
    },
    {
      "x": 0,
      "y": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/polygon": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    },
    {
      "x": 0,
      "y": 2
    }
  ]
}
```

## Minimum Enclosing Point Circle API

USD 3.00 per job.

Find the smallest circle containing a supplied set of points. 1–24 distinct integer planar points within one million. Exact candidate centers, squared-radius comparisons and containment; approximate center/radius plus exact rational center and squared radius. Collinear sets and singletons supported; no weighted disks. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Bounding_volumes/index.html). No endorsement is implied.

Example input:

```json
{
  "points": [
    {
      "x": -1,
      "y": 0
    },
    {
      "x": 1,
      "y": 0
    },
    {
      "x": 0,
      "y": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/center": {
    "x": 0,
    "y": 0
  },
  "/squaredRadius": {
    "n": "1",
    "d": "1"
  },
  "/radius": 1
}
```

## Minimum Area Oriented Rectangle API

USD 3.00 per job.

Find a smallest-area rectangle enclosing planar points. 1–64 distinct integer points within one million. Exact hull-edge projection and area comparisons; approximate counterclockwise corners and exact rational area. Degenerate point or line rectangles allowed; equal-area orientation uses first hull edge. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Bounding_volumes/group__PkgBoundingVolumesRef.html). No endorsement is implied.

Example input:

```json
{
  "points": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    },
    {
      "x": 2,
      "y": 1
    },
    {
      "x": 0,
      "y": 1
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/area": {
    "n": "2",
    "d": "1"
  },
  "/corners": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    },
    {
      "x": 2,
      "y": 1
    },
    {
      "x": 0,
      "y": 1
    }
  ]
}
```

## Convex Polygon Miter Offset API

USD 3.00 per job.

Offset every edge of a convex polygon outward by a supplied distance. Strictly convex counterclockwise integer polygon, 3–32 vertices within one million; distance 0–10000 and miter ratio limit 1–10000. Approximate Euclidean line intersections with a checked miter ceiling. Outward straight-edge joins only; no rounded corners or inward erosion. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Straight_skeleton_2/index.html). No endorsement is implied.

Example input:

```json
{
  "polygon": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    },
    {
      "x": 2,
      "y": 2
    },
    {
      "x": 0,
      "y": 2
    }
  ],
  "distance": 1,
  "miterLimit": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/polygon": [
    {
      "x": -1,
      "y": -1
    },
    {
      "x": 3,
      "y": -1
    },
    {
      "x": 3,
      "y": 3
    },
    {
      "x": -1,
      "y": 3
    }
  ]
}
```

## B Spline de Boor Evaluation API

USD 3.00 per job.

Evaluate a planar B spline at supplied parameter values. Degree 0–5, 1–32 control points, nondecreasing knots with exact count and multiplicity at most degree plus one. First and last base spans must have positive width. Parameters lie in the closed base interval; the right endpoint uses the last span. Approximate de Boor evaluation, no extrapolation or rational weights. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.html). No endorsement is implied.

Example input:

```json
{
  "degree": 1,
  "controlPoints": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 2
    }
  ],
  "knots": [
    0,
    0,
    1,
    1
  ],
  "parameters": [
    0,
    0.25,
    1
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/points": [
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 0.5,
      "y": 0.5
    },
    {
      "x": 2,
      "y": 2
    }
  ]
}
```

## Polygon Obstacle Shortest Path API

USD 3.00 per job.

Find a shortest Euclidean path around convex polygon obstacles. Up to 6 disjoint strictly convex counterclockwise integer obstacles, 32 total vertices, coordinates within one million. Start and end strictly outside obstacles. Exact visibility predicates allow boundary travel; approximate edge lengths and shortest path. Obstacles must not touch; planar point motion only. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Visibility_2/index.html). No endorsement is implied.

Example input:

```json
{
  "start": {
    "x": -1,
    "y": 1
  },
  "end": {
    "x": 3,
    "y": 1
  },
  "obstacles": [
    [
      {
        "x": 0,
        "y": 0
      },
      {
        "x": 2,
        "y": 0
      },
      {
        "x": 2,
        "y": 2
      },
      {
        "x": 0,
        "y": 2
      }
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/length": 4.82842712474619,
  "/path": [
    {
      "x": -1,
      "y": 1
    },
    {
      "x": 0,
      "y": 0
    },
    {
      "x": 2,
      "y": 0
    },
    {
      "x": 3,
      "y": 1
    }
  ]
}
```

## Triangle Mesh Plane Section API

USD 3.00 per job.

Intersect each triangle of a mesh with an exact plane. Up to 128 integer vertices and 256 nondegenerate triangular faces, coordinates within one million; integer plane coefficients within one million and offset within one billion. Exact rational per-face segments or tangent points; duplicate shared sections retained. Coplanar faces rejected; no closed-loop stitching or solid-volume claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [doc.cgal.org](https://doc.cgal.org/latest/Polygon_mesh_processing/index.html). No endorsement is implied.

Example input:

```json
{
  "vertices": [
    {
      "x": 0,
      "y": 0,
      "z": -1
    },
    {
      "x": 2,
      "y": 0,
      "z": 1
    },
    {
      "x": 0,
      "y": 2,
      "z": 1
    }
  ],
  "triangles": [
    [
      0,
      1,
      2
    ]
  ],
  "plane": {
    "a": 0,
    "b": 0,
    "c": 1,
    "d": 0
  }
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/sections/0/kind": "segment",
  "/sections/0/points": [
    {
      "x": {
        "n": "1",
        "d": "1"
      },
      "y": {
        "n": "0",
        "d": "1"
      },
      "z": {
        "n": "0",
        "d": "1"
      }
    },
    {
      "x": {
        "n": "0",
        "d": "1"
      },
      "y": {
        "n": "1",
        "d": "1"
      },
      "z": {
        "n": "0",
        "d": "1"
      }
    }
  ]
}
```

## LL1 Predictive Token Parser API

USD 3.00 per job.

Build a predictive grammar table and parse a supplied token sequence. Up to 16 nonterminals, 32 terminals, 64 productions and 128 tokens; identifier symbols and empty productions supported. Compute nullable, FIRST and FOLLOW sets; reject left recursion and table conflicts. At most 1024 expansion steps; no lexical scanning or error recovery. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cornell.edu](https://www.cs.cornell.edu/courses/cs4120/2023sp/notes/topdown/). No endorsement is implied.

Example input:

```json
{
  "nonterminals": [
    "S"
  ],
  "terminals": [
    "a",
    "b"
  ],
  "start": "S",
  "productions": [
    {
      "lhs": "S",
      "rhs": [
        "a",
        "S",
        "b"
      ]
    },
    {
      "lhs": "S",
      "rhs": []
    }
  ],
  "tokens": [
    "a",
    "a",
    "b",
    "b"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/accepted": true,
  "/productionTrace": [
    0,
    0,
    1
  ]
}
```

## Earley Context Free Recognizer API

USD 3.00 per job.

Recognize tokens under a general context-free grammar. Up to 16 nonterminals, 32 terminals, 64 productions and 64 tokens. Empty rules, ambiguity and left recursion supported; recognition and chart-state counts only. Reject beyond 20000 states or two million work steps. No parse forest, lexical scanning or probabilistic interpretation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.nltk.org](https://www.nltk.org/api/nltk.parse.earleychart.html). No endorsement is implied.

Example input:

```json
{
  "nonterminals": [
    "S"
  ],
  "terminals": [
    "a",
    "b"
  ],
  "start": "S",
  "productions": [
    {
      "lhs": "S",
      "rhs": [
        "a",
        "S",
        "b"
      ]
    },
    {
      "lhs": "S",
      "rhs": []
    }
  ],
  "tokens": [
    "a",
    "a",
    "b",
    "b"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/accepted": true
}
```

## Thompson Regex AST Compiler API

USD 3.00 per job.

Compile a regular-expression syntax tree to an epsilon NFA and match tokens. Postorder tree with up to 128 nodes: literal, epsilon, concatenation, union and star. Literal symbols are whole tokens; at most 128 input tokens. Return explicit automaton and acceptance. No pattern-string parser, backreferences, lookaround or execution of supplied code. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [swtch.com](https://swtch.com/~rsc/regexp/regexp1.html). No endorsement is implied.

Example input:

```json
{
  "nodes": [
    {
      "kind": "literal",
      "name": "a",
      "children": []
    },
    {
      "kind": "star",
      "name": "",
      "children": [
        0
      ]
    },
    {
      "kind": "literal",
      "name": "b",
      "children": []
    },
    {
      "kind": "concat",
      "name": "",
      "children": [
        1,
        2
      ]
    }
  ],
  "tokens": [
    "a",
    "a",
    "b"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/accepted": true,
  "/stateCount": 8
}
```

## Deterministic Pushdown Trace API

USD 3.00 per job.

Replay a deterministic pushdown automaton over token input. Up to 16 states and symbols, 128 transitions and input tokens, 512 steps and stack depth 128. Null input means epsilon; null top matches an empty stack. Push lists are bottom-to-top. Reject epsilon/consuming conflicts; acceptance requires halted execution, consumed input and a final state. No nondeterministic search. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ocw.mit.edu](https://ocw.mit.edu/courses/18-404j-theory-of-computation-fall-2020/). No endorsement is implied.

Example input:

```json
{
  "states": [
    "q",
    "f"
  ],
  "inputAlphabet": [
    "a"
  ],
  "stackAlphabet": [
    "Z"
  ],
  "start": "q",
  "initialStack": [
    "Z"
  ],
  "finalStates": [
    "f"
  ],
  "transitions": [
    {
      "state": "q",
      "symbol": "a",
      "top": "Z",
      "to": "f",
      "push": []
    }
  ],
  "tokens": [
    "a"
  ],
  "stepLimit": 8
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/accepted": true,
  "/finalState": "f",
  "/finalStack": []
}
```

## First Order Term Unification API

USD 3.00 per job.

Find a most-general substitution for finite first-order term equations. Up to 128 postorder variable/function nodes and 64 equations. Variables share names; function name and arity define a symbol. Occurs check rejects infinite terms. Return normalized prefix terms or a clash reason; 100000 work steps and 16000-character substitution ceiling. No higher-order, associative or commutative unification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cornell.edu](https://www.cs.cornell.edu/courses/cs4110/2016fa/lectures/lecture23.pdf). No endorsement is implied.

Example input:

```json
{
  "nodes": [
    {
      "kind": "variable",
      "name": "x",
      "children": []
    },
    {
      "kind": "function",
      "name": "a",
      "children": []
    },
    {
      "kind": "function",
      "name": "f",
      "children": [
        0,
        1
      ]
    },
    {
      "kind": "function",
      "name": "b",
      "children": []
    },
    {
      "kind": "variable",
      "name": "y",
      "children": []
    },
    {
      "kind": "function",
      "name": "f",
      "children": [
        3,
        4
      ]
    }
  ],
  "equations": [
    [
      2,
      5
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/unifiable": true,
  "/substitutions": [
    {
      "variable": "x",
      "term": "b"
    },
    {
      "variable": "y",
      "term": "a"
    }
  ]
}
```

## Hindley Milner Type Inference API

USD 3.00 per job.

Infer principal types for a small lambda-calculus syntax tree. Postorder trees up to 128 nodes: variables, lambda, application, nonrecursive polymorphic let and integer/boolean literals. Closed terms only; occurs check and fresh let instantiation. Type errors returned explicitly; 100000 work steps and bounded type rendering. No recursion, effects, subtyping, classes or user-code execution. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cornell.edu](https://www.cs.cornell.edu/courses/cs312/2005sp/lectures/rec22.asp). No endorsement is implied.

Example input:

```json
{
  "nodes": [
    {
      "kind": "variable",
      "name": "x",
      "children": []
    },
    {
      "kind": "lambda",
      "name": "x",
      "children": [
        0
      ]
    },
    {
      "kind": "variable",
      "name": "id",
      "children": []
    },
    {
      "kind": "variable",
      "name": "id",
      "children": []
    },
    {
      "kind": "apply",
      "name": "",
      "children": [
        2,
        3
      ]
    },
    {
      "kind": "let",
      "name": "id",
      "children": [
        1,
        4
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/typeable": true,
  "/principalType": "('a -> 'a)"
}
```

## Propositional Resolution Proof Checker API

USD 3.00 per job.

Check every claimed resolvent in a propositional proof. Up to 64 initial clauses, 128 proof steps and variables 1–32. Signed literals, set semantics and explicit oriented pivot: left contains pivot, right its negation. Each step cites earlier clauses. Return the first invalid step and whether a valid empty clause proves contradiction; no SAT search or premise-truth certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cmu.edu](https://www.cs.cmu.edu/~15414/s25/lectures/14-resolution.pdf). No endorsement is implied.

Example input:

```json
{
  "clauses": [
    [
      1
    ],
    [
      -1
    ]
  ],
  "steps": [
    {
      "left": 0,
      "right": 1,
      "pivot": 1,
      "claimed": []
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/valid": true,
  "/contradiction": true,
  "/clauses": [
    [
      1
    ],
    [
      -1
    ],
    []
  ]
}
```

## Reduced Ordered BDD Builder API

USD 3.00 per job.

Build a canonical reduced ordered decision diagram for a Boolean truth table. 1–12 distinct variables and exactly 2 to that count Boolean values. Table rows follow binary order with the first variable most significant. Terminal IDs 0/1; eliminate equal branches and share identical ordered nodes. Return satisfying assignment count. No symbolic formula parser or reordering search. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.cmu.edu](https://www.cs.cmu.edu/~bryant/pubdir/iccad95.pdf). No endorsement is implied.

Example input:

```json
{
  "variables": [
    "a",
    "b"
  ],
  "values": [
    false,
    true,
    true,
    false
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/root": 4,
  "/satisfyingAssignments": "2",
  "/nodes": [
    {
      "id": 2,
      "variable": "b",
      "low": 0,
      "high": 1
    },
    {
      "id": 3,
      "variable": "b",
      "low": 1,
      "high": 0
    },
    {
      "id": 4,
      "variable": "a",
      "low": 2,
      "high": 3
    }
  ]
}
```

## Bounded Petri Marking Reachability API

USD 3.00 per job.

Explore reachable markings of a capacity-constrained Petri net. 1–8 places, up to 16 consume/produce transitions, capacities 0–1024, depth 0–32 and at most 1024 states. Breadth-first exploration stays within supplied capacities and returns a shortest target firing sequence. Complete=false identifies an unexplored depth frontier; exceeding the state ceiling rejects. No unbounded-net or temporal property proof. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www2.informatik.uni-hamburg.de](https://www2.informatik.uni-hamburg.de/tgi/PetriNets/introductions/). No endorsement is implied.

Example input:

```json
{
  "initial": [
    1,
    0
  ],
  "target": [
    0,
    1
  ],
  "capacities": [
    1,
    1
  ],
  "transitions": [
    {
      "consume": [
        1,
        0
      ],
      "produce": [
        0,
        1
      ]
    }
  ],
  "maxSteps": 4,
  "stateLimit": 32
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/reachable": true,
  "/targetSequence": [
    0
  ],
  "/complete": true,
  "/states": [
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ]
}
```

## Finite Trace Temporal Logic API

USD 3.00 per job.

Evaluate a temporal formula at every position of a supplied finite trace. Postorder formula tree up to 128 nodes and trace length 1–256. Support propositions, Boolean operators, strong next, eventually, always, until and release. Next is false at the final position; release is the finite-trace dual of until. Return the root truth vector; no infinite-trace model checking or prediction. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ojs.aaai.org](https://ojs.aaai.org/index.php/AAAI/article/download/8872/8731). No endorsement is implied.

Example input:

```json
{
  "nodes": [
    {
      "kind": "proposition",
      "name": "a",
      "children": []
    },
    {
      "kind": "eventually",
      "name": "",
      "children": [
        0
      ]
    }
  ],
  "trace": [
    [],
    [
      "a"
    ],
    []
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/satisfied": true,
  "/truthAtPositions": [
    true,
    true,
    false
  ]
}
```

## Bounded Linear Program Vertex Optimum

USD 3.00 per job.

Solve a small box-bounded linear program and return a primal/dual witness. Up to five variables and eight additional inequalities. Explicit finite box bounds; minimizes or maximizes the stated linear objective. Enumerates active bases and requires primal feasibility and nonnegative KKT multipliers. Infeasible or numerically unresolved inputs are rejected before checkout; no unboundedness certificate or integer-program claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html). No endorsement is implied.

Example input:

```json
{
  "lower": [
    0,
    0
  ],
  "upper": [
    4,
    4
  ],
  "constraints": [
    {
      "coefficients": [
        1,
        1
      ],
      "bound": 4
    },
    {
      "coefficients": [
        1,
        0
      ],
      "bound": 2
    }
  ],
  "objective": [
    3,
    2
  ],
  "direction": "maximize"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/point": [
    2,
    2
  ],
  "/objectiveValue": 10,
  "/multipliers": [
    2,
    1
  ]
}
```

## Strictly Convex Quadratic Optimum

USD 3.00 per job.

Solve a small strictly convex quadratic program with a verified active-set witness. Objective one-half x-transpose H x plus linear-transpose x. Symmetric well-conditioned positive-definite Hessian, finite box and supplied linear inequalities. Enumerates active sets and requires feasible KKT stationarity and nonnegative multipliers. Nonconvex, infeasible or numerically unresolved inputs reject before checkout. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [web.stanford.edu](https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf). No endorsement is implied.

Example input:

```json
{
  "lower": [
    0,
    0
  ],
  "upper": [
    10,
    10
  ],
  "constraints": [
    {
      "coefficients": [
        1,
        1
      ],
      "bound": 4
    }
  ],
  "hessian": [
    [
      2,
      0
    ],
    [
      0,
      2
    ]
  ],
  "linear": [
    -4,
    -6
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/point": [
    1.5,
    2.5
  ],
  "/objectiveValue": -12.5,
  "/multipliers": [
    1
  ]
}
```

## Nonnegative Least-Squares Fit

USD 3.00 per job.

Fit nonnegative coefficients and expose residual and optimality evidence. At most eight columns and sixty-four rows; full-column-rank, adequately conditioned supplied design required. Exhaustive support search and KKT checks for the squared Euclidean residual objective. Not a statistical significance test; singular or unresolved inputs reject before checkout. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.nnls.html). No endorsement is implied.

Example input:

```json
{
  "design": [
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ],
  "response": [
    -1,
    2
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coefficients": [
    0,
    2
  ],
  "/squaredError": 1,
  "/gradient": [
    1,
    0
  ],
  "/positiveColumns": [
    1
  ]
}
```

## Weighted Geometric Median

USD 3.00 per job.

Locate a weighted Euclidean median with a convergence residual. Modified Weiszfeld update handles iterates coincident with data points. Weights are normalized for the subgradient stopping test; the objective retains supplied weights. Up to one hundred twenty-eight points, five dimensions and one thousand iterations. Nonconvergence rejects before checkout; a flat minimizer need not be unique. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [statweb.rutgers.edu](https://statweb.rutgers.edu/cunhui/papers/43.pdf). No endorsement is implied.

Example input:

```json
{
  "points": [
    [
      -1,
      0
    ],
    [
      1,
      0
    ],
    [
      0,
      -1
    ],
    [
      0,
      1
    ]
  ],
  "weights": [
    1,
    1,
    1,
    1
  ],
  "tolerance": 1e-8,
  "maxIterations": 500
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/point": [
    0,
    0
  ],
  "/weightedDistance": 4,
  "/normalizedSubgradientResidual": 0
}
```

## Reduced Tall-Matrix Factorization

USD 3.00 per job.

Factor a supplied tall matrix and report reconstruction and orthogonality evidence. Real tall matrices with at most six columns and thirty-two rows. Full column rank and condition number at most ten thousand; symmetric Jacobi diagonalization of the Gram matrix. Singular values descend; vector signs are normalized. Nonconvergence or failed residual checks reject before checkout. No general rank-deficient or complex factorization claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.svd.html). No endorsement is implied.

Example input:

```json
{
  "matrix": [
    [
      3,
      0
    ],
    [
      0,
      2
    ],
    [
      0,
      0
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/singularValues": [
    3,
    2
  ],
  "/u": [
    [
      1,
      0
    ],
    [
      0,
      1
    ],
    [
      0,
      0
    ]
  ],
  "/vt": [
    [
      1,
      0
    ],
    [
      0,
      1
    ]
  ],
  "/conditionNumber": 1.5
}
```

## Small Dense Matrix Exponential

USD 3.00 per job.

Evaluate the exponential of a supplied square matrix. At most six dimensions and matrix one-norm at most sixteen. Original bounded scaling-and-squaring Taylor implementation, not the cited package’s Padé algorithm. Series tail bound covers truncation of the scaled series in exact arithmetic, not all floating-point or squaring error. No external execution or differential-equation certification. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.expm.html). No endorsement is implied.

Example input:

```json
{
  "matrix": [
    [
      0,
      1
    ],
    [
      0,
      0
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/exponential": [
    [
      1,
      1
    ],
    [
      0,
      1
    ]
  ],
  "/scalingSteps": 1
}
```

## Bounded Real Prony Model

USD 3.00 per job.

Recover one or two separated real exponential components from equally spaced samples. Hankel recurrence and Vandermonde amplitude recovery; distinct positive real poles from 0.0001 through two. All supplied samples must reproduce within a relative residual of one in ten million. Complex, repeated, close or unresolved poles and noisy model mismatch reject before checkout. Extrapolation is conditional, without a prediction guarantee. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.colorado.edu](https://www.colorado.edu/amath/sites/default/files/attached-files/bey-mon-2005.pdf). No endorsement is implied.

Example input:

```json
{
  "samples": [
    3,
    5,
    9,
    17
  ],
  "order": 2,
  "forecastSteps": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/poles": [
    1,
    2
  ],
  "/amplitudes": [
    1,
    2
  ],
  "/forecast": [
    33,
    65
  ]
}
```

## Padé Taylor Approximation

USD 3.00 per job.

Construct a rational approximation matching supplied ascending Taylor coefficients. Numerator and denominator degrees through six; denominator normalized to constant one. Requires exactly m+n+1 Taylor coefficients. Singular matching systems and evaluation at poles or near poles reject before checkout. Matching coefficients does not establish global approximation error or analytic continuation. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.pade.html). No endorsement is implied.

Example input:

```json
{
  "taylorCoefficients": [
    1,
    1,
    0.5
  ],
  "numeratorDegree": 1,
  "denominatorDegree": 1,
  "evaluationPoints": [
    0,
    1
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/numerator": [
    1,
    0.5
  ],
  "/denominator": [
    1,
    -0.5
  ],
  "/values": [
    1,
    3
  ],
  "/coefficientMatchingResidual": 0
}
```

## Linear Kalman Filter Replay

USD 3.00 per job.

Replay supplied state and observation models with stable covariance updates. Predict then update for each observation, at most four state/measurement dimensions and sixty-four steps. Symmetric semidefinite initial/process covariance and conditioned positive-definite measurement/innovation covariance required. Joseph update; PSD eigenvalue roundoff tolerance is relative to matrix norm, without an absolute variance floor. Negative variances and materially indefinite matrices reject before checkout. No parameter estimation, sensor integration or nonlinear filter. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [ipnpr.jpl.nasa.gov](https://ipnpr.jpl.nasa.gov/progress_report/42-233/42-233A-orig.pdf). No endorsement is implied.

Example input:

```json
{
  "transition": [
    [
      1
    ]
  ],
  "observation": [
    [
      1
    ]
  ],
  "processCovariance": [
    [
      0
    ]
  ],
  "measurementCovariance": [
    [
      1
    ]
  ],
  "initialMean": [
    0
  ],
  "initialCovariance": [
    [
      1
    ]
  ],
  "observations": [
    [
      2
    ],
    [
      2
    ]
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/states/0/mean/0": 1,
  "/states/0/covariance/0/0": 0.5,
  "/states/1/mean/0": 1.3333333333333333,
  "/states/1/covariance/0/0": 0.3333333333333333
}
```

## Savitzky–Golay Coefficient Plan

USD 3.00 per job.

Prepare centered polynomial smoothing or derivative weights. Odd windows from three through thirty-one samples, polynomial degree through eight below window length and derivative order no larger than degree. Weights are left-to-right dot-product coefficients, not reversed convolution coefficients. Uniform spacing and centered evaluation only; failed conditioning or polynomial reproduction rejects before checkout. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [docs.scipy.org](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.savgol_coeffs.html). No endorsement is implied.

Example input:

```json
{
  "windowLength": 5,
  "polynomialOrder": 2,
  "derivativeOrder": 0,
  "sampleSpacing": 1
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/coefficients": [
    -0.08571428571428572,
    0.34285714285714286,
    0.4857142857142857,
    0.34285714285714286,
    -0.08571428571428572
  ],
  "/positions": [
    -2,
    -1,
    0,
    1,
    2
  ]
}
```

## Suffix Array and LCP Index

USD 3.00 per job.

Build suffix order, adjacent longest-common-prefix lengths and a distinct-substring count. At most4096 well-formed Unicode code points. Positions/counts are code-point based, case sensitive, with no normalization or empty suffix. Rank doubling and Kasai LCP; no file or corpus access. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [algs4.cs.princeton.edu](https://algs4.cs.princeton.edu/63suffix/SuffixArray.java.html). No endorsement is implied.

Example input:

```json
{
  "text": "banana"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/suffixArray": [
    5,
    3,
    1,
    0,
    4,
    2
  ],
  "/lcp": [
    0,
    1,
    3,
    0,
    0,
    2
  ],
  "/distinctSubstringCount": 15
}
```

## Palindromic Substring Index

USD 3.00 per job.

Find every odd/even palindrome radius, total occurrences and an earliest longest palindrome. At most4096 well-formed Unicode code points; case sensitive, no normalization. Odd radii include their center, even radii are half lengths centered before each position. Count occurrences including single points. Empty text has an empty longest match. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [dl.acm.org](https://dl.acm.org/doi/10.1145/321892.321896). No endorsement is implied.

Example input:

```json
{
  "text": "abba"
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/oddRadii": [
    1,
    1,
    1,
    1
  ],
  "/evenRadii": [
    0,
    0,
    2,
    0
  ],
  "/longest": {
    "start": 0,
    "length": 4,
    "text": "abba"
  },
  "/palindromicSubstringCount": 6
}
```

## Three-Way Line Merge Preview

USD 3.00 per job.

Combine nonconflicting line edits from two versions of a common base and expose conflicts. Each input is at most128 lines,1000 characters per line, also shared byte/node limits. Deterministic LCS ties prefer base deletion. Touching replacement ranges commute, but an insertion at a replacement boundary is conservatively conflicting. Identical replacements coalesce. Any conflict makes mergedLines null; nothing is applied and no full Git-equivalence is claimed. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [git-scm.com](https://git-scm.com/docs/git-merge-file). No endorsement is implied.

Example input:

```json
{
  "base": [
    "a",
    "b",
    "c"
  ],
  "left": [
    "A",
    "b",
    "c"
  ],
  "right": [
    "a",
    "b",
    "C"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/clean": true,
  "/mergedLines": [
    "A",
    "b",
    "C"
  ],
  "/conflicts": []
}
```

## Functional Dependency Candidate Keys

USD 3.00 per job.

Compute attribute closure and all inclusion-minimal keys implied by supplied dependencies. One through12 distinct attributes, at most64 dependencies. Empty determinant and empty candidate key are allowed when implied. Enumerate at most4096 subsets in cardinality/input-order bit-mask order; list keys in that order. Logical supplied dependencies only, not an inferred data-quality or normalization certificate. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [cs.stanford.edu](https://cs.stanford.edu/~ullman/fcdb/spr99/lec13.pdf). No endorsement is implied.

Example input:

```json
{
  "attributes": [
    "A",
    "B",
    "C"
  ],
  "dependencies": [
    {
      "left": [
        "A"
      ],
      "right": [
        "B"
      ]
    },
    {
      "left": [
        "B"
      ],
      "right": [
        "C"
      ]
    }
  ],
  "closureOf": [
    "A"
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/closure": [
    "A",
    "B",
    "C"
  ],
  "/candidateKeys": [
    [
      "A"
    ]
  ],
  "/superkeyCount": 4
}
```

## Positive Datalog Fixed Point

USD 3.00 per job.

Evaluate finite function-free positive rules to a least fixed point over supplied facts. At most128 ground facts,32 rules,16 predicates/constants, arity1..3, four body atoms and six variables per rule. Terms ?Uppercase are variables; other allowed identifiers are constants. Head variables must occur in the body. No negation, functions, aggregates or external facts. Reject before checkout above1024 total facts,8192 intermediate bindings or200000 join attempts. passes is rule-order-dependent iteration work, not proof depth. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [abiteboul.com](https://abiteboul.com/TEACHING/DBCOURSE/). No endorsement is implied.

Example input:

```json
{
  "facts": [
    {
      "predicate": "edge",
      "args": [
        "a",
        "b"
      ]
    },
    {
      "predicate": "edge",
      "args": [
        "b",
        "c"
      ]
    }
  ],
  "rules": [
    {
      "head": {
        "predicate": "path",
        "args": [
          "?X",
          "?Y"
        ]
      },
      "body": [
        {
          "predicate": "edge",
          "args": [
            "?X",
            "?Y"
          ]
        }
      ]
    },
    {
      "head": {
        "predicate": "path",
        "args": [
          "?X",
          "?Z"
        ]
      },
      "body": [
        {
          "predicate": "path",
          "args": [
            "?X",
            "?Y"
          ]
        },
        {
          "predicate": "edge",
          "args": [
            "?Y",
            "?Z"
          ]
        }
      ]
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/derivedFactCount": 3
}
```

## De Bruijn Token Sequence

USD 3.00 per job.

Construct a cyclic sequence containing every fixed-length alphabet word exactly once. One through eight distinct caller-ordered tokens, each at most16 characters, and order1..8. Alphabet-size to the order is at most8192. Return cyclic tokens and the prefix-extended linear sequence; token positions, not concatenated characters, define windows. Deterministic necklace construction; no randomization or cryptographic use. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.sciencedirect.com](https://www.sciencedirect.com/science/article/pii/0012365X7890002X). No endorsement is implied.

Example input:

```json
{
  "alphabet": [
    "0",
    "1"
  ],
  "order": 2
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/cyclicTokens": [
    "0",
    "0",
    "1",
    "1"
  ],
  "/linearTokens": [
    "0",
    "0",
    "1",
    "1",
    "0"
  ],
  "/windowCount": 4
}
```

## Static Perfect Hash Plan

USD 3.00 per job.

Prepare a collision-free affine lookup table for a bounded fixed integer key set. One through64 unique integer keys in[0,2147483646]; at most128 queries. Search4096 affine parameter pairs spread deterministically across prime2147483647 into n-squared slots. Reject if this bounded search finds no placement. Return stored keys so nonmember queries compare equality; not a minimal perfect hash or the full FKS linear-space construction. Exact modular arithmetic. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.princeton.edu](https://www.cs.princeton.edu/courses/archive/fall09/cos521/Handouts/storingasparse.pdf). No endorsement is implied.

Example input:

```json
{
  "keys": [
    1,
    2,
    3
  ],
  "queries": [
    2,
    4
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/multiplier": 1,
  "/offset": 0,
  "/prime": "2147483647",
  "/queries": [
    {
      "key": 2,
      "slot": 2,
      "found": true
    },
    {
      "key": 4,
      "slot": 4,
      "found": false
    }
  ]
}
```

## Misra-Gries Heavy Hitter Summary

USD 3.00 per job.

Identify frequent token candidates with bounded counters and verify them in a second pass. Up to2048 tokens of1..32 characters,2..64 buckets, plus shared byte/node limits. The first pass has at most buckets-minus-one counters; a second pass returns exact candidate counts. Every frequency strictly above n/buckets is retained. Counter upper bounds add the number of full-decrement passes. No persistent stream or approximate claim about unlisted below-threshold items. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [www.cs.utexas.edu](https://www.cs.utexas.edu/~misra/scannedPdf.dir/FindRepeatedElements.pdf). No endorsement is implied.

Example input:

```json
{
  "tokens": [
    "a",
    "a",
    "a",
    "b",
    "a",
    "c"
  ],
  "buckets": 3
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/processed": 6,
  "/decrementPasses": 1,
  "/candidates": [
    {
      "token": "a",
      "counter": 3,
      "exactCount": 4,
      "upperBound": 4
    }
  ],
  "/heavyHitters": [
    "a"
  ]
}
```

## HyperLogLog Register Profile

USD 3.00 per job.

Build a reproducible cardinality sketch from supplied unsigned32-bit hashes. Up to2048 prehashed integers, precision4..10. Upper bits choose registers; leading-zero suffix rank is capped at33-minus-precision. Original alpha constants and small/large-range corrections; a saturated32-bit correction returns null. The1.04/sqrt(m) error is a model approximation, not measured accuracy. Requires suitably uniform independent input hashes; no hashing, exact cardinality, privacy or cryptographic guarantee. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [algo.inria.fr](https://algo.inria.fr/flajolet/Publications/FlFuGaMe07.pdf). No endorsement is implied.

Example input:

```json
{
  "hashes": [],
  "precision": 4
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/registers": [
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0
  ],
  "/zeroRegisters": 16,
  "/estimate": 0,
  "/correction": "linear-counting",
  "/relativeStandardError": 0.26
}
```

## Wavelet Matrix Range Queries

USD 3.00 per job.

Build a16-level wavelet matrix and answer equality, less-than and order-statistic range queries. Up to2048 unsigned16-bit values and128 queries over half-open[start,end) ranges. Zero-based k returns null when it exceeds the selected range length, including empty ranges. Each level exposes its stable-partition bit string and zero count. Static in-memory data only; no persistent index, compression-ratio or logarithmic build-time claim. Supplied non-sensitive data only; no live account access, automated changes or certification. Profile 1.0.0: approximate non-integers use 12 significant digits; safe integers and declared integer strings are preserved.

Reference: [users.dcc.uchile.cl](https://users.dcc.uchile.cl/~gnavarro/abstracts/is14.html). No endorsement is implied.

Example input:

```json
{
  "values": [
    3,
    1,
    4,
    1,
    5
  ],
  "queries": [
    {
      "start": 1,
      "end": 5,
      "value": 1,
      "k": 2
    }
  ]
}
```

Selected expected result fields (JSON pointers):

```json
{
  "/answers": [
    {
      "start": 1,
      "end": 5,
      "countEqual": 2,
      "countLess": 0,
      "kth": 4
    }
  ]
}
```