{ "id": "assignment-cost-optimize", "name": "Exact fixed-slot cost assignment", "description": "Choose an exact minimum-cost complete one-job-per-slot assignment over caller-declared nonoverlapping slots and admissible edges, with lexical ties and a verifiable optimum or Hall-deficiency certificate. No live availability check, reservation or job dispatch.", "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": [ "Assign independent jobs to fixed slots at minimum total cost", "Optimize exact one-to-one job and slot pairing with forbidden assignments" ], "whenToUse": [ "Caller declares all admissible edges and pairwise nonoverlapping slots in one time coordinate system" ], "whenNotToUse": [ "General precedence or resource scheduling, overlapping slots, travel-time or skill inference", "Live calendar availability, slot reservation, real job dispatch, payments or currency conversion" ], "capabilities": [ "Exact decimal BigInt optimization with lexical slot-ID ties in sorted job order", "Complete assignments and start-ordered inert schedules with residual-potential optimum certificates", "Maximum cardinality and a Hall-deficient job-set witness when no complete schedule exists", "Pure full evaluation before payment challenge; valid infeasible results contain no usable schedule" ], "related": [ "workflow-resource-plan", "interval-analyze" ], "limits": { "inputBytes": 100000, "outputBytes": 400000, "jsonNodes": 12000, "depth": 20, "jobs": 16, "slots": 32, "edges": 512, "tickMaximum": 1000000000000, "decimalIntegerDigits": 12, "decimalFractionDigits": 6, "vertices": 50, "residualArcs": 1120, "augmentations": 16, "maximumVertexSelectionChecks": 40000, "maximumEdgeRelaxationChecks": 17920 }, "errorCodes": [ "INPUT_LIMIT", "OUTPUT_LIMIT", "COMPLEXITY_LIMIT", "INVALID_JSON", "INVALID_NUMBER", "INVALID_UNICODE", "UNSAFE_KEY", "DUPLICATE_ID", "INVALID_SLOT", "OVERLAPPING_SLOTS", "UNKNOWN_EDGE_ID", "DUPLICATE_EDGE", "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": "assignment-cost-optimize", "operation.category": "workflow-assurance", "limit.httpRequestBytes": 131072, "limit.requestBytes": 100000, "limit.responseBytes": 524288, "limit.resultBytes": 400000, "limit.jsonDepth": 20, "limit.jsonNodes": 12000, "assignment.profile": "fixed-slot-exact-assignment-v1", "assignment.maxJobs": 16, "assignment.maxSlots": 32, "assignment.maxEdges": 512, "assignment.maxDecimalIntegerDigits": 12, "assignment.maxDecimalFractionDigits": 6, "assignment.slotModel": "pairwise-nonoverlapping-half-open-fixed-slots", "assignment.objective": "minimum-total-caller-declared-cost", "assignment.tieBreak": "lexicographic-slot-id-vector-in-utf16-job-id-order", "assignment.exactOptimality": true, "assignment.feasibilityGuaranteed": false, "assignment.binaryFloatCosts": false, "assignment.generalResourceScheduling": false, "assignment.dependenciesInferred": false, "assignment.availabilityVerified": false, "assignment.reservesSlots": false, "assignment.executesSchedule": false, "input.jobIds.maxItems": 16, "input.jobIds.minItems": 1, "input.slots.maxItems": 32, "input.slots.minItems": 1, "input.edges.maxItems": 512, "input.timeUnit.maxLength": 100, "input.timeUnit.minLength": 1, "input.timeOrigin.maxLength": 100, "input.timeOrigin.minLength": 1, "input.costUnit.maxLength": 100, "input.costUnit.minLength": 1 }, "unknownPolicy": "Undeclared requirements are unknown, never compatible. Matching declared facts does not establish semantic fit or input validity.", "preflight": "/preflight" }, "documentation": "/reference/tools/assignment-cost-optimize.md", "serviceContract": "/reference/services/assignment-cost-optimize.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/assignment-cost-optimize", "mpp": "/v1/mpp/assignment-cost-optimize" }, "inputSchema": { "$schema": "https://json-schema.org/draft/2020-12/schema", "type": "object", "properties": { "jobIds": { "minItems": 1, "maxItems": 16, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "slots": { "minItems": 1, "maxItems": 32, "type": "array", "items": { "type": "object", "properties": { "id": { "type": "string", "minLength": 1, "maxLength": 100 }, "start": { "type": "integer", "minimum": 0, "maximum": 1000000000000 }, "end": { "type": "integer", "minimum": 0, "maximum": 1000000000000 } }, "required": [ "id", "start", "end" ], "additionalProperties": false } }, "edges": { "maxItems": 512, "type": "array", "items": { "type": "object", "properties": { "jobId": { "type": "string", "minLength": 1, "maxLength": 100 }, "slotId": { "type": "string", "minLength": 1, "maxLength": 100 }, "cost": { "type": "string", "pattern": "^(?:0|[1-9][0-9]{0,11})(?:\\.[0-9]{1,6})?$" } }, "required": [ "jobId", "slotId", "cost" ], "additionalProperties": false } }, "timeUnit": { "type": "string", "minLength": 1, "maxLength": 100 }, "timeOrigin": { "type": "string", "minLength": 1, "maxLength": 100 }, "costUnit": { "type": "string", "minLength": 1, "maxLength": 100 } }, "required": [ "jobIds", "slots", "edges", "timeUnit", "timeOrigin", "costUnit" ], "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "operation", "version", "result", "provenance" ], "properties": { "operation": { "const": "assignment-cost-optimize", "type": "string" }, "version": { "const": "0.29.0", "type": "string" }, "result": { "$schema": "https://json-schema.org/draft/2020-12/schema", "oneOf": [ { "type": "object", "properties": { "profile": { "type": "string", "const": "fixed-slot-exact-assignment-v1" }, "externalRequests": { "type": "number", "const": 0 }, "execution": { "type": "boolean", "const": false }, "availabilityVerified": { "type": "boolean", "const": false }, "timeUnit": { "type": "string", "minLength": 1, "maxLength": 100 }, "timeOrigin": { "type": "string", "minLength": 1, "maxLength": 100 }, "costUnit": { "type": "string", "minLength": 1, "maxLength": 100 }, "jobIds": { "minItems": 1, "maxItems": 16, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "slotIds": { "minItems": 1, "maxItems": 32, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "status": { "type": "string", "const": "optimal" }, "assignments": { "minItems": 1, "maxItems": 16, "type": "array", "items": { "type": "object", "properties": { "jobId": { "type": "string", "minLength": 1, "maxLength": 100 }, "slotId": { "type": "string", "minLength": 1, "maxLength": 100 }, "start": { "type": "integer", "minimum": 0, "maximum": 1000000000000 }, "end": { "type": "integer", "minimum": 0, "maximum": 1000000000000 }, "cost": { "type": "string", "pattern": "^(?:0|[1-9][0-9]{0,11})(?:\\.[0-9]{1,6})?$" } }, "required": [ "jobId", "slotId", "start", "end", "cost" ], "additionalProperties": false } }, "schedule": { "minItems": 1, "maxItems": 16, "type": "array", "items": { "type": "object", "properties": { "jobId": { "type": "string", "minLength": 1, "maxLength": 100 }, "slotId": { "type": "string", "minLength": 1, "maxLength": 100 }, "start": { "type": "integer", "minimum": 0, "maximum": 1000000000000 }, "end": { "type": "integer", "minimum": 0, "maximum": 1000000000000 }, "cost": { "type": "string", "pattern": "^(?:0|[1-9][0-9]{0,11})(?:\\.[0-9]{1,6})?$" } }, "required": [ "jobId", "slotId", "start", "end", "cost" ], "additionalProperties": false } }, "unusedSlotIds": { "maxItems": 31, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "totalCost": { "type": "object", "properties": { "numerator": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "denominator": { "type": "string", "pattern": "^[1-9][0-9]*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, "certificate": { "type": "object", "properties": { "kind": { "type": "string", "const": "min-cost-flow-potentials" }, "scale": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "primaryMultiplier": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "tieBase": { "type": "integer", "minimum": 2, "maximum": 33 }, "combinedCost": { "type": "string", "pattern": "^(?:0|[1-9][0-9]*)$" }, "vertexPotentials": { "minItems": 4, "maxItems": 50, "type": "array", "items": { "type": "string", "pattern": "^(?:0|-?[1-9][0-9]*)$" } }, "requiredFlow": { "type": "integer", "minimum": 1, "maximum": 16 }, "achievedFlow": { "type": "integer", "minimum": 1, "maximum": 16 } }, "required": [ "kind", "scale", "primaryMultiplier", "tieBase", "combinedCost", "vertexPotentials", "requiredFlow", "achievedFlow" ], "additionalProperties": false } }, "required": [ "profile", "externalRequests", "execution", "availabilityVerified", "timeUnit", "timeOrigin", "costUnit", "jobIds", "slotIds", "status", "assignments", "schedule", "unusedSlotIds", "totalCost", "certificate" ], "additionalProperties": false }, { "type": "object", "properties": { "profile": { "type": "string", "const": "fixed-slot-exact-assignment-v1" }, "externalRequests": { "type": "number", "const": 0 }, "execution": { "type": "boolean", "const": false }, "availabilityVerified": { "type": "boolean", "const": false }, "timeUnit": { "type": "string", "minLength": 1, "maxLength": 100 }, "timeOrigin": { "type": "string", "minLength": 1, "maxLength": 100 }, "costUnit": { "type": "string", "minLength": 1, "maxLength": 100 }, "jobIds": { "minItems": 1, "maxItems": 16, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "slotIds": { "minItems": 1, "maxItems": 32, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "status": { "type": "string", "const": "infeasible" }, "schedule": { "type": "null" }, "maximumCardinality": { "type": "integer", "minimum": 0, "maximum": 15 }, "witness": { "type": "object", "properties": { "kind": { "type": "string", "const": "hall-deficiency" }, "jobIds": { "minItems": 1, "maxItems": 16, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "neighborSlotIds": { "maxItems": 32, "type": "array", "items": { "type": "string", "minLength": 1, "maxLength": 100 } }, "deficiency": { "type": "integer", "minimum": 1, "maximum": 16 }, "maximumMatching": { "maxItems": 15, "type": "array", "items": { "type": "object", "properties": { "jobId": { "type": "string", "minLength": 1, "maxLength": 100 }, "slotId": { "type": "string", "minLength": 1, "maxLength": 100 } }, "required": [ "jobId", "slotId" ], "additionalProperties": false } } }, "required": [ "kind", "jobIds", "neighborSlotIds", "deficiency", "maximumMatching" ], "additionalProperties": false } }, "required": [ "profile", "externalRequests", "execution", "availabilityVerified", "timeUnit", "timeOrigin", "costUnit", "jobIds", "slotIds", "status", "schedule", "maximumCardinality", "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": { "jobIds": [ "a", "b", "c" ], "slots": [ { "id": "s1", "start": 0, "end": 10 }, { "id": "s2", "start": 10, "end": 20 }, { "id": "s3", "start": 20, "end": 30 } ], "edges": [ { "jobId": "a", "slotId": "s1", "cost": "7" }, { "jobId": "a", "slotId": "s2", "cost": "1" }, { "jobId": "a", "slotId": "s3", "cost": "4" }, { "jobId": "b", "slotId": "s1", "cost": "2" }, { "jobId": "b", "slotId": "s2", "cost": "6" }, { "jobId": "b", "slotId": "s3", "cost": "5" }, { "jobId": "c", "slotId": "s1", "cost": "3" }, { "jobId": "c", "slotId": "s2", "cost": "4" }, { "jobId": "c", "slotId": "s3", "cost": "1" } ], "timeUnit": "minute", "timeOrigin": "caller-defined zero", "costUnit": "model cost units" }, "exampleResponse": { "operation": "assignment-cost-optimize", "version": "0.29.0", "result": { "profile": "fixed-slot-exact-assignment-v1", "externalRequests": 0, "execution": false, "availabilityVerified": false, "timeUnit": "minute", "timeOrigin": "caller-defined zero", "costUnit": "model cost units", "jobIds": [ "a", "b", "c" ], "slotIds": [ "s1", "s2", "s3" ], "status": "optimal", "assignments": [ { "jobId": "a", "slotId": "s2", "start": 10, "end": 20, "cost": "1" }, { "jobId": "b", "slotId": "s1", "start": 0, "end": 10, "cost": "2" }, { "jobId": "c", "slotId": "s3", "start": 20, "end": 30, "cost": "1" } ], "schedule": [ { "jobId": "b", "slotId": "s1", "start": 0, "end": 10, "cost": "2" }, { "jobId": "a", "slotId": "s2", "start": 10, "end": 20, "cost": "1" }, { "jobId": "c", "slotId": "s3", "start": 20, "end": 30, "cost": "1" } ], "unusedSlotIds": [], "totalCost": { "numerator": "4", "denominator": "1" }, "certificate": { "kind": "min-cost-flow-potentials", "scale": "1", "primaryMultiplier": "64", "tieBase": 4, "combinedCost": "274", "vertexPotentials": [ "0", "48", "0", "62", "128", "128", "128", "128" ], "requiredFlow": 3, "achievedFlow": 3 } }, "provenance": { "inputSha256": "f9e5201837d942fee4208f1463702123eb7efe360904719bc8393f0680cdfd7f", "outputSha256": "e078060ea2c9b79dfff96c4e2bcff3a77cd038736ab4285f0d4d4561e1e2065f", "deterministic": true, "externalRequests": 0 } }, "requiredHeaders": { "Content-Type": "application/json", "Idempotency-Key": "random 16–128 character operation identifier" }, "fixedExample": "/reference/examples/assignment-cost-optimize.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." } }