{ "id": "cost-matrix-round", "name": "Exact two-margin matrix rounding", "description": "Round a supplied decimal allocation matrix to exact integer floor/ceiling cells while preserving both declared margins, minimizing absolute error and breaking ties lexicographically; return a verifiable optimum or infeasibility witness. No payments, accounting advice or execution.", "category": "workflow-assurance", "priceUsd": "0.01", "pricingStatus": "proposed-unverified", "pricing": { "unit": "one successful operation call", "proposedNominalUsd": "0.01", "sixDecimalTokenBaseUnits": "10000", "subscription": false, "includesPayerWalletOrNetworkFees": false, "liveQuoteVerified": false, "condition": "Actual SDK challenge is authoritative only within the caller's explicit authorization; configured six-decimal token peg is an operator assertion, not a conversion guarantee." }, "intents": [ "Round fractional allocations while preserving row and column totals", "Reconcile a supplied allocation matrix into integer minor units" ], "whenToUse": [ "Caller supplies both exact margins and requires the minimum absolute rounding error" ], "whenNotToUse": [ "Actual financial allocation, posting ledgers, payments or accounting advice", "Automatically choosing margins or unconstrained proportional apportionment" ], "capabilities": [ "Exact decimal BigInt arithmetic with deterministic UTF-16 ID order", "Independent residual-potential optimum certificates or bounded infeasibility witnesses", "Well-formed infeasible inputs return no usable matrix; pure full evaluation before payment challenge" ], "related": [ "integer-apportion", "gfm-table-compose" ], "limits": { "inputBytes": 100000, "outputBytes": 400000, "jsonNodes": 12000, "depth": 20, "rows": 8, "columns": 8, "cells": 64, "decimalIntegerDigits": 18, "decimalFractionDigits": 6, "targetDigits": 24, "vertices": 18, "residualArcs": 160, "augmentations": 64, "maximumRelaxationChecks": 176960 }, "errorCodes": [ "INPUT_LIMIT", "OUTPUT_LIMIT", "COMPLEXITY_LIMIT", "INVALID_JSON", "INVALID_NUMBER", "INVALID_UNICODE", "UNSAFE_KEY", "DUPLICATE_ID", "MATRIX_DIMENSIONS", "MARGIN_TOTAL_MISMATCH", "INTERNAL_CERTIFICATE" ], "requirementsProfile": { "format": "declared-requirements-v1", "facts": { "execution.suppliedCode": false, "execution.remoteMutation": false, "execution.llmInference": false, "execution.paidMcp": false, "verification.semanticTruth": false, "verification.sourceAuthenticity": false, "verification.liveVulnerabilities": false, "numbers.arbitraryPrecisionJson": false, "numbers.model": "ieee754-binary64", "privacy.requestBodyPersisted": false, "execution.deterministic": true, "execution.networkAccess": false, "privacy.resultBodyPersisted": false, "payment.x402": true, "payment.mpp": true, "operation.id": "cost-matrix-round", "operation.category": "workflow-assurance", "limit.httpRequestBytes": 131072, "limit.requestBytes": 100000, "limit.responseBytes": 524288, "limit.resultBytes": 400000, "limit.jsonDepth": 20, "limit.jsonNodes": 12000, "matrixRound.profile": "exact-two-margin-round-v1", "matrixRound.maxRows": 8, "matrixRound.maxColumns": 8, "matrixRound.maxCells": 64, "matrixRound.maxDecimalIntegerDigits": 18, "matrixRound.maxDecimalFractionDigits": 6, "matrixRound.objective": "minimum-total-absolute-error", "matrixRound.tieBreak": "lexicographic-row-major-after-utf16-id-sort", "matrixRound.cellChoices": "floor-or-ceiling", "matrixRound.margins": "caller-declared-row-and-column-targets", "matrixRound.exactOptimality": true, "matrixRound.feasibilityGuaranteed": false, "matrixRound.binaryFloatAmounts": false, "matrixRound.executesAllocation": false, "matrixRound.accountingAdvice": false, "matrixRound.availabilityVerified": false, "input.rowIds.maxItems": 8, "input.rowIds.minItems": 1, "input.columnIds.maxItems": 8, "input.columnIds.minItems": 1, "input.values.maxItems": 8, "input.values.minItems": 1, "input.rowTargets.maxItems": 8, "input.rowTargets.minItems": 1, "input.columnTargets.maxItems": 8, "input.columnTargets.minItems": 1 }, "unknownPolicy": "Undeclared requirements are unknown, never compatible. Matching declared facts does not establish semantic fit or input validity.", "preflight": "/preflight" }, "documentation": "/reference/tools/cost-matrix-round.md", "serviceContract": "/reference/services/cost-matrix-round.json", "errors": [ { "status": 400, "meaning": "Malformed JSON, missing/invalid idempotency key, or payment identifier mismatch", "retry": "Correct the request before payment" }, { "status": 402, "meaning": "Payment challenge or rejected payment", "retry": "Use official protocol SDK; inspect payment outcome before another payment" }, { "status": 409, "meaning": "Idempotency conflict, duplicate proof, or PAYMENT_UNCERTAIN", "retry": "Keep original key, body, and proof; reconcile uncertainty with operator; never blindly repay" }, { "status": 413, "meaning": "Input or generated output too large", "retry": "Reduce input; no payment attempted for validation failure" }, { "status": 415, "meaning": "Unsupported media type or compression", "retry": "Send uncompressed application/json" }, { "status": 422, "meaning": "Schema or service-specific semantic validation failure", "retry": "Correct input using returned error code; no payment attempted" }, { "status": 429, "meaning": "Request/payment-attempt rate exceeded", "retry": "Wait for rate limit window; preserve existing payment identity" }, { "status": 503, "meaning": "Payment configuration/provider/state unavailable, or live DNS preparation failed before settlement", "retry": "Check readiness; DNS preparation failures may retry the identical key/body/credential only; uncertainty requires reconciliation" } ], "numericPrecision": "JavaScript IEEE-754 numbers; use strings for large integer IDs/exact decimals where the schema accepts strings. No lossless numeric parsing.", "paymentWorkflow": { "discoveryOnly": false, "supportedProtocols": [ "x402", "mpp" ], "x402": { "credentialHeader": "PAYMENT-SIGNATURE", "challengeHeader": "PAYMENT-REQUIRED", "receiptHeader": "PAYMENT-RESPONSE", "version": 2, "scheme": "exact", "paymentIdentifier": "payment-identifier extension MUST equal the HTTP Idempotency-Key", "sdk": "@x402/core with @x402/evm" }, "mpp": { "supported": true, "credentialHeader": "Authorization", "challengeHeader": "WWW-Authenticate", "receiptHeader": "Payment-Receipt", "method": "tempo", "intent": "charge", "sdk": "mppx", "tokenDecimals": 6 }, "steps": [ "Check configured readiness and the exact service schema", "Generate a fresh random Idempotency-Key for this operation; never use a discovery probe fixture for purchases", "Send valid input without a credential to obtain the official protocol challenge", "Use the official SDK and authorized wallet to fulfill the challenge", "Retry only with identical key, body, protocol and credential", "On PAYMENT_UNCERTAIN stop and request operator reconciliation; never blindly pay again" ], "versionedRetries": "Request fingerprint includes service release version. Retries across a version upgrade can conflict; coordinate upgrades outside the 24-hour replay window and reconcile pending attempts.", "docs": "/llms.txt" }, "method": "POST", "paths": { "x402": "/v1/x402/cost-matrix-round", "mpp": "/v1/mpp/cost-matrix-round" }, "inputSchema": { "$schema": "https://json-schema.org/draft/2020-12/schema", "type": "object", "properties": { "rowIds": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "columnIds": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "values": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]{0,17})(?:\\.[0-9]{1,6})?$" } } }, "rowTargets": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]{0,23})$" } }, "columnTargets": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]{0,23})$" } } }, "required": [ "rowIds", "columnIds", "values", "rowTargets", "columnTargets" ], "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "operation", "version", "result", "provenance" ], "properties": { "operation": { "const": "cost-matrix-round", "type": "string" }, "version": { "const": "0.29.0", "type": "string" }, "result": { "$schema": "https://json-schema.org/draft/2020-12/schema", "oneOf": [ { "type": "object", "properties": { "profile": { "type": "string", "const": "exact-two-margin-round-v1" }, "externalRequests": { "type": "number", "const": 0 }, "execution": { "type": "boolean", "const": false }, "availabilityVerified": { "type": "boolean", "const": false }, "rowIds": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "columnIds": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "rowTargets": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } }, "columnTargets": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } }, "status": { "type": "string", "const": "optimal" }, "matrix": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } } }, "rowTotals": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } }, "columnTotals": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } }, "grandTotal": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "absoluteError": { "type": "object", "properties": { "numerator": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "denominator": { "type": "string", "pattern": "^[1-9][0-9]*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, "cells": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "object", "properties": { "floor": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "fraction": { "type": "object", "properties": { "numerator": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "denominator": { "type": "string", "pattern": "^[1-9][0-9]*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, "increment": { "type": "integer", "minimum": 0, "maximum": 1 } }, "required": [ "floor", "fraction", "increment" ], "additionalProperties": false } } }, "certificate": { "type": "object", "properties": { "kind": { "type": "string", "const": "min-cost-flow-potentials" }, "scale": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "primaryMultiplier": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "combinedCost": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "vertexPotentials": { "minItems": 4, "maxItems": 18, "type": "array", "items": { "type": "string", "pattern": "^(?:0|-?[1-9][0-9]*)$" } }, "requiredFlow": { "type": "integer", "minimum": 0, "maximum": 64 }, "achievedFlow": { "type": "integer", "minimum": 0, "maximum": 64 } }, "required": [ "kind", "scale", "primaryMultiplier", "combinedCost", "vertexPotentials", "requiredFlow", "achievedFlow" ], "additionalProperties": false } }, "required": [ "profile", "externalRequests", "execution", "availabilityVerified", "rowIds", "columnIds", "rowTargets", "columnTargets", "status", "matrix", "rowTotals", "columnTotals", "grandTotal", "absoluteError", "cells", "certificate" ], "additionalProperties": false }, { "type": "object", "properties": { "profile": { "type": "string", "const": "exact-two-margin-round-v1" }, "externalRequests": { "type": "number", "const": 0 }, "execution": { "type": "boolean", "const": false }, "availabilityVerified": { "type": "boolean", "const": false }, "rowIds": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "columnIds": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "rowTargets": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } }, "columnTargets": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } }, "status": { "type": "string", "const": "infeasible" }, "matrix": { "type": "null" }, "witness": { "oneOf": [ { "type": "object", "properties": { "kind": { "type": "string", "const": "margin-bound" }, "axis": { "type": "string", "enum": [ "row", "column" ] }, "id": { "type": "string", "minLength": 1, "maxLength": 100 }, "target": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "minimum": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "maximum": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" } }, "required": [ "kind", "axis", "id", "target", "minimum", "maximum" ], "additionalProperties": false }, { "type": "object", "properties": { "kind": { "type": "string", "const": "residual-min-cut" }, "reachableRowIds": { "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "reachableColumnIds": { "maxItems": 8, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "requiredFlow": { "type": "integer", "minimum": 0, "maximum": 64 }, "achievedFlow": { "type": "integer", "minimum": 0, "maximum": 64 }, "cutCapacity": { "type": "integer", "minimum": 0, "maximum": 64 }, "partialIncrements": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "minItems": 1, "maxItems": 8, "type": "array", "items": { "type": "integer", "minimum": 0, "maximum": 1 } } } }, "required": [ "kind", "reachableRowIds", "reachableColumnIds", "requiredFlow", "achievedFlow", "cutCapacity", "partialIncrements" ], "additionalProperties": false } ] } }, "required": [ "profile", "externalRequests", "execution", "availabilityVerified", "rowIds", "columnIds", "rowTargets", "columnTargets", "status", "matrix", "witness" ], "additionalProperties": false } ] }, "provenance": { "type": "object", "required": [ "inputSha256", "outputSha256", "deterministic", "externalRequests" ], "properties": { "inputSha256": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "outputSha256": { "type": "string", "pattern": "^[a-f0-9]{64}$" }, "deterministic": { "const": true }, "externalRequests": { "const": 0 } } } }, "additionalProperties": false }, "exampleInput": { "rowIds": [ "r1", "r2" ], "columnIds": [ "a", "b", "c" ], "values": [ [ "0.6", "0.6", "0.8" ], [ "0.4", "0.4", "0.2" ] ], "rowTargets": [ "2", "1" ], "columnTargets": [ "1", "1", "1" ] }, "exampleResponse": { "operation": "cost-matrix-round", "version": "0.29.0", "result": { "profile": "exact-two-margin-round-v1", "externalRequests": 0, "execution": false, "availabilityVerified": false, "rowIds": [ "r1", "r2" ], "columnIds": [ "a", "b", "c" ], "rowTargets": [ "2", "1" ], "columnTargets": [ "1", "1", "1" ], "status": "optimal", "matrix": [ [ "0", "1", "1" ], [ "1", "0", "0" ] ], "rowTotals": [ "2", "1" ], "columnTotals": [ "1", "1", "1" ], "grandTotal": "3", "absoluteError": { "numerator": "12", "denominator": "5" }, "cells": [ [ { "floor": "0", "fraction": { "numerator": "3", "denominator": "5" }, "increment": 0 }, { "floor": "0", "fraction": { "numerator": "3", "denominator": "5" }, "increment": 1 }, { "floor": "0", "fraction": { "numerator": "4", "denominator": "5" }, "increment": 1 } ], [ { "floor": "0", "fraction": { "numerator": "2", "denominator": "5" }, "increment": 1 }, { "floor": "0", "fraction": { "numerator": "2", "denominator": "5" }, "increment": 0 }, { "floor": "0", "fraction": { "numerator": "1", "denominator": "5" }, "increment": 0 } ] ], "certificate": { "kind": "min-cost-flow-potentials", "scale": "10", "primaryMultiplier": "64", "combinedCost": "1564", "vertexPotentials": [ "-772", "-530", "-772", "0", "-2", "0", "0" ], "requiredFlow": 3, "achievedFlow": 3 } }, "provenance": { "inputSha256": "15594a17c74c1a6c9b7cd6f0f74ea731fd6a8c6a10f59eab883541f893d56dfa", "outputSha256": "ac4a933060b7d1d3b3d7d2bb32f7a9a4ef7ba15111ac766bb16a59be2976ee2a", "deterministic": true, "externalRequests": 0 } }, "requiredHeaders": { "Content-Type": "application/json", "Idempotency-Key": "random 16–128 character operation identifier" }, "fixedExample": "/reference/examples/cost-matrix-round.json", "execution": { "deterministic": true, "externalRequests": 0, "maxExternalRequests": 0, "resultSnapshotPersisted": false, "fixedExampleIsIllustrativeSnapshot": false, "requiresPayment": true, "supportsMcpExecution": false }, "releaseSnapshot": { "format": "static-release-reference-v1", "sourceVersion": "0.29.0", "sourceRegistrySha256": "a2b5ec09bf6c38b9d2879d746a4fded374f5928b445377b0270ef6aa8e6cac65", "generatedAt": "2026-10-06T15:38:00Z", "releaseAcceptance": "not-verified-by-generator", "runtimeReadiness": "not-evaluated", "livePaymentsVerified": false, "indexingVerified": false, "apiOrigin": null, "notice": "Build-time release reference. Runtime readiness, deployment, payment settlement and external indexing are not evaluated here. Prices are proposed; this file cannot authorize execution or payment." } }