# Relocation, container circulation, exact algebra and raster encoding

## Slot Relocation Move Plan

Plan ordered asset moves between declared single-occupancy slots. Supply sourceRevision, slots with unique IDs, initialPlacements and exactly one desiredPlacements assignment for every initially placed asset. Slot and asset identities are opaque, case-sensitive ASCII labels of 1 to 48 letters, digits, underscores, periods, colons, pipes or hyphens. Every slot reference must be declared; each asset and occupied or desired slot is unique. Set the required nullable bufferSlotId field to null for no designated buffer, or name a declared slot that is initially empty and is never desired. The policy repeatedly moves the first asset in initial placement order whose desired slot is empty. When only closed cycles remain, it moves the first remaining asset to the designated buffer, then resumes desired moves. Fixed placements need no move; a swap needs three moves and a three-asset cycle needs four. If any closed cycle needs a buffer and none is designated, the whole request returns blocked with its cycles, zero orderedMoves and identical initial and final inventories, including any acyclic work that otherwise could proceed. Other unused empty slots are not temporary buffers under this policy. A blocked result describes this restricted move policy, not physical impossibility. Inventory retains declared slot order, unchangedAssets contains assets with no proposed move, and blocked cycle traversal follows initial placement order. Up to 128 declared slots and 128 assets are supported within the shared 36,000-byte, 6,000-node, depth-24 input profile and 500,000-byte output guard. These are workload bounds. Duplicate or unknown identities and an occupied or desired buffer reject the whole request during preflight. This deterministic supplied-record plan does not move anything, authorize work, model travel, weight, access or handling constraints, prove physical feasibility, or promise global optimality. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Request example](slot-relocation-move-plan.request.example.json) · [Input schema](slot-relocation-move-plan.input.schema.json) · [Result schema](slot-relocation-move-plan.result.schema.json)

## Reusable Container Circulation Plan

Plan reusable container assignments across dispatch, return and cleaning times. Supply sourceRevision, declared types and locations, containers with exact typeId, locationId and readyMinute, and demands with exact dispatch and return locations, dispatchMinute, returnMinute, cleaningMinutes, quantity and priority. IDs are opaque, case-sensitive ASCII labels of 1 to 48 letters, digits, underscores, periods, colons, pipes or hyphens. All numeric fields are nonnegative safe whole integers in one common minute timeline; each return is strictly after dispatch and return plus cleaning must remain a safe integer. Demands run by earliest dispatchMinute, then lower numeric priority, then supplied demand order. Each demand uses only the exact type and dispatch location with readyMinute at or before dispatch; candidates are chosen by earliest readyMinute and then supplied container order. The entire requested quantity is allocated or the demand returns shortage with no reservations or state changes. A shortage leaves containers available to later demands, and zero quantity needs none. Assigned containers become available at the declared return location exactly at returnMinute plus cleaningMinutes. The report includes ordered demand plans, individual circulation assignments and final container availability in original container order. Total requested quantity counts every demand, allocatedQuantity counts assignments including repeated reuse, and unallocatedQuantity counts all units of shortage demands, not only their numeric shortage. The deterministic greedy ordering is disclosed and is not a global optimum or forecast of future demand. A final location is the location at final modeled availability, not an observed physical location at a common wall-clock time. Up to 128 types, locations, containers and demands and 512 total requested units are supported within the shared 36,000-byte, 6,000-node, depth-24 input profile and 500,000-byte output guard. These are input and result workload bounds. Duplicate IDs, unknown references, invalid timing and unsafe return-plus-cleaning reject the whole request during preflight, even for a demand that would have a shortage. This supplied-record plan does not dispatch or reserve containers, authorize work, infer transit between locations, prove cleaning or physical availability, or promise optimal allocation. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Request example](reusable-container-circulation-plan.request.example.json) · [Input schema](reusable-container-circulation-plan.input.schema.json) · [Result schema](reusable-container-circulation-plan.result.schema.json)

## Bivariate Rational Groebner Basis

Compute the reduced monic Groebner basis over exact rational coefficients for two ordered variables using lexicographic order, first variable greater, and query normal forms and ideal membership. Supply 1–8 sparse generators and 0–8 queries, each at most16 terms, initial total degree at most8, integer numerator magnitude and positive denominator at most1000000. Zero polynomials are empty arrays. Duplicate terms combine and fractions normalize. The zero ideal has an empty basis; the unit ideal has basis[1]. Intermediate guards reject rather than truncate: 512-bit coefficients, total degree64, 16 basis polynomials, 512 simultaneously stored sparse terms, 2048 pairs and 200000 budgeted operations. These conservative computation limits can reject an input within the initial profile. No symbolic expression parsing or external algebra system. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Request example](bivariate-rational-groebner-basis.request.example.json) · [Input schema](bivariate-rational-groebner-basis.input.schema.json) · [Result schema](bivariate-rational-groebner-basis.result.schema.json)

## QOI RGBA Raster Encoder

Encode supplied unpremultiplied row-major RGBA8 pixels as a complete QOI1.0 file in lowercase hexadecimal, with channels4, supplied colorspace0 or1 and at most1024 pixels. Return the header, complete byte length and counts of emitted chunks. Deterministic opcode priority is RUN, INDEX, DIFF, LUMA, RGB, RGBA, with signed modulo256 differences and runs of at most62 pixels. The selection is deterministic and does not promise the globally smallest encoding. No image decoding, color conversion or filesystem access. Use authorized, non-sensitive data. The report describes supplied records and does not change external systems.

[Request example](qoi-rgba-raster-encoder.request.example.json) · [Input schema](qoi-rgba-raster-encoder.input.schema.json) · [Result schema](qoi-rgba-raster-encoder.result.schema.json)

One-time job. See the exact service price before checkout. Save your private JSON result within its 30-day access period.
Requests accept at most 36,000 UTF-8 input bytes. Send only authorized, non-sensitive records.

For a known hosted offer, read current checkout and wallet availability with `GET https://gatewayinformationgroup.com/api/catalog/v1/search?id=PRODUCT_ID`. Then use the input schema and request example above.

Use the existing [agent checkout guide](https://gatewayinformationgroup.com/developers) to prepare a quote, pay and retrieve the private result.