{
  "id": "rectangle-set-compose",
  "name": "Exact integer rectangle set algebra",
  "description": "Compose union, intersection, A-minus-B difference or XOR of declared axis-aligned half-open integer rectangles into deterministic x-first disjoint rectangles, exact integer area and bounds.",
  "category": "data-assurance",
  "priceUsd": "0.006",
  "pricingStatus": "proposed-unverified",
  "pricing": {
    "unit": "one successful operation call",
    "proposedNominalUsd": "0.006",
    "sixDecimalTokenBaseUnits": "6000",
    "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": [
    "union intersect subtract xor rectangular regions",
    "subtract declared exclusions from page tile regions",
    "create canonical disjoint rectangles and exact area"
  ],
  "whenToUse": [
    "Exact set algebra over caller-supplied Cartesian integer regions",
    "Generating disjoint drawing or selection data from axis-aligned half-open rectangles",
    "Computing exact coordinate-squared area beyond JavaScript safe integers"
  ],
  "whenNotToUse": [
    "Rotated shapes, arbitrary polygons, geographic or geodesic area, CRS or units conversion",
    "Image modification, masking, redaction or identifying actual objects",
    "Click safety, collision physics, optimal packing or minimum-rectangle decomposition",
    "Fetching sources, writing files, model calls, target execution or changing external state"
  ],
  "capabilities": [
    "Exact canonical decimal-string coordinates and BigInt arithmetic",
    "Operand unions ignore input ordering and duplicate coverage",
    "X-first interval sweep merges touching selected y intervals and identical intervals across consecutive x slabs",
    "Canonical disjoint output sorted numerically with half-open bounds and exact area",
    "Deterministic supplied-input-only inert artifact; no network, clock, randomness or external state change"
  ],
  "related": [
    "interval-analyze"
  ],
  "limits": {
    "inputBytes": 100000,
    "outputBytes": 300000,
    "jsonNodes": 10000,
    "depth": 20,
    "profile": "integer-half-open-rectangle-sets-v1",
    "inputRectangles": 32,
    "absoluteCoordinate": "1000000000000",
    "xEndpoints": 64,
    "yEndpoints": 64,
    "elementaryCells": 3969,
    "resultRectangles": 1024,
    "outputCoordinateStrings": 4096,
    "sweepWork": 100000
  },
  "errorCodes": [
    "INPUT_LIMIT",
    "OUTPUT_LIMIT",
    "COMPLEXITY_LIMIT",
    "INVALID_JSON",
    "INVALID_NUMBER",
    "INVALID_UNICODE",
    "UNSAFE_KEY",
    "INVALID_INPUT",
    "RECTANGLE_COUNT_LIMIT",
    "RECTANGLE_COORDINATE_RANGE",
    "RECTANGLE_EXTENT",
    "RECTANGLE_WORK_LIMIT",
    "RECTANGLE_OUTPUT_LIMIT"
  ],
  "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": "rectangle-set-compose",
      "operation.category": "data-assurance",
      "limit.httpRequestBytes": 131072,
      "limit.requestBytes": 100000,
      "limit.responseBytes": 524288,
      "limit.resultBytes": 300000,
      "limit.jsonDepth": 20,
      "limit.jsonNodes": 10000,
      "geometry.profile": "integer-half-open-rectangle-sets-v1",
      "geometry.coordinateModel": "caller-integer-grid",
      "geometry.boundary": "half-open",
      "geometry.coordinateMin": "-1000000000000",
      "geometry.coordinateMax": "1000000000000",
      "geometry.exactIntegerArea": true,
      "geometry.areaUnits": "caller-grid-units-squared",
      "geometry.maxInputRectangles": 32,
      "geometry.maxXEndpoints": 64,
      "geometry.maxYEndpoints": 64,
      "geometry.maxElementaryCells": 3969,
      "geometry.maxResultRectangles": 1024,
      "geometry.maxOutputCoordinateStrings": 4096,
      "geometry.maxSweepWork": 100000,
      "geometry.decomposition": "x-first-identical-y-interval-merging",
      "geometry.minimumRectangleCover": false,
      "geometry.geodesicArea": false,
      "geometry.arbitraryPolygons": false,
      "geometry.rotatedRectangles": false,
      "geometry.crsConversion": false,
      "geometry.physicalUnitsInferred": false,
      "geometry.imageRedaction": false,
      "geometry.clickSafety": false,
      "geometry.objectRecognition": false,
      "input.a.maxItems": 32,
      "input.b.maxItems": 32
    },
    "unknownPolicy": "Undeclared requirements are unknown, never compatible. Matching declared facts does not establish semantic fit or input validity.",
    "preflight": "/preflight"
  },
  "documentation": "/reference/tools/rectangle-set-compose.md",
  "serviceContract": "/reference/services/rectangle-set-compose.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/rectangle-set-compose",
    "mpp": "/v1/mpp/rectangle-set-compose"
  },
  "inputSchema": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "operation": {
        "type": "string",
        "enum": [
          "union",
          "intersection",
          "difference",
          "xor"
        ]
      },
      "a": {
        "maxItems": 32,
        "type": "array",
        "items": {
          "type": "array",
          "prefixItems": [
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            },
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            },
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            },
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            }
          ],
          "items": false,
          "minItems": 4,
          "maxItems": 4
        }
      },
      "b": {
        "maxItems": 32,
        "type": "array",
        "items": {
          "type": "array",
          "prefixItems": [
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            },
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            },
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            },
            {
              "type": "string",
              "maxLength": 14,
              "pattern": "^(?:0|-?[1-9][0-9]*)$"
            }
          ],
          "items": false,
          "minItems": 4,
          "maxItems": 4
        }
      }
    },
    "required": [
      "operation",
      "a",
      "b"
    ],
    "additionalProperties": false
  },
  "outputSchema": {
    "type": "object",
    "required": [
      "operation",
      "version",
      "result",
      "provenance"
    ],
    "properties": {
      "operation": {
        "const": "rectangle-set-compose",
        "type": "string"
      },
      "version": {
        "const": "0.29.0",
        "type": "string"
      },
      "result": {
        "$schema": "https://json-schema.org/draft/2020-12/schema",
        "type": "object",
        "properties": {
          "profile": {
            "type": "string",
            "const": "integer-half-open-rectangle-sets-v1"
          },
          "operation": {
            "type": "string",
            "enum": [
              "union",
              "intersection",
              "difference",
              "xor"
            ]
          },
          "coordinateModel": {
            "type": "string",
            "const": "caller-integer-grid"
          },
          "boundary": {
            "type": "string",
            "const": "half-open"
          },
          "rectangles": {
            "maxItems": 1024,
            "type": "array",
            "items": {
              "type": "array",
              "prefixItems": [
                {
                  "type": "string",
                  "maxLength": 14,
                  "pattern": "^(?:0|-?[1-9][0-9]*)$"
                },
                {
                  "type": "string",
                  "maxLength": 14,
                  "pattern": "^(?:0|-?[1-9][0-9]*)$"
                },
                {
                  "type": "string",
                  "maxLength": 14,
                  "pattern": "^(?:0|-?[1-9][0-9]*)$"
                },
                {
                  "type": "string",
                  "maxLength": 14,
                  "pattern": "^(?:0|-?[1-9][0-9]*)$"
                }
              ],
              "items": false,
              "minItems": 4,
              "maxItems": 4
            }
          },
          "area": {
            "type": "string",
            "maxLength": 25,
            "pattern": "^(?:0|[1-9][0-9]*)$"
          },
          "bounds": {
            "anyOf": [
              {
                "type": "array",
                "prefixItems": [
                  {
                    "type": "string",
                    "maxLength": 14,
                    "pattern": "^(?:0|-?[1-9][0-9]*)$"
                  },
                  {
                    "type": "string",
                    "maxLength": 14,
                    "pattern": "^(?:0|-?[1-9][0-9]*)$"
                  },
                  {
                    "type": "string",
                    "maxLength": 14,
                    "pattern": "^(?:0|-?[1-9][0-9]*)$"
                  },
                  {
                    "type": "string",
                    "maxLength": 14,
                    "pattern": "^(?:0|-?[1-9][0-9]*)$"
                  }
                ],
                "items": false,
                "minItems": 4,
                "maxItems": 4
              },
              {
                "type": "null"
              }
            ]
          }
        },
        "required": [
          "profile",
          "operation",
          "coordinateModel",
          "boundary",
          "rectangles",
          "area",
          "bounds"
        ],
        "additionalProperties": false
      },
      "provenance": {
        "type": "object",
        "required": [
          "inputSha256",
          "outputSha256",
          "deterministic",
          "externalRequests"
        ],
        "properties": {
          "inputSha256": {
            "type": "string",
            "pattern": "^[a-f0-9]{64}$"
          },
          "outputSha256": {
            "type": "string",
            "pattern": "^[a-f0-9]{64}$"
          },
          "deterministic": {
            "const": true
          },
          "externalRequests": {
            "const": 0
          }
        }
      }
    },
    "additionalProperties": false
  },
  "exampleInput": {
    "operation": "difference",
    "a": [
      [
        "0",
        "0",
        "6",
        "4"
      ]
    ],
    "b": [
      [
        "2",
        "1",
        "4",
        "3"
      ]
    ]
  },
  "exampleResponse": {
    "operation": "rectangle-set-compose",
    "version": "0.29.0",
    "result": {
      "profile": "integer-half-open-rectangle-sets-v1",
      "operation": "difference",
      "coordinateModel": "caller-integer-grid",
      "boundary": "half-open",
      "rectangles": [
        [
          "0",
          "0",
          "2",
          "4"
        ],
        [
          "2",
          "0",
          "4",
          "1"
        ],
        [
          "2",
          "3",
          "4",
          "4"
        ],
        [
          "4",
          "0",
          "6",
          "4"
        ]
      ],
      "area": "20",
      "bounds": [
        "0",
        "0",
        "6",
        "4"
      ]
    },
    "provenance": {
      "inputSha256": "78c60701985f51c5f58fd98603b34f2205596ce461af7da13a1083c7454b8021",
      "outputSha256": "069c4ac83e8387a1f235ddd7b78bccbdfbf2592a44e19809a782352db0e4712c",
      "deterministic": true,
      "externalRequests": 0
    }
  },
  "requiredHeaders": {
    "Content-Type": "application/json",
    "Idempotency-Key": "random 16–128 character operation identifier"
  },
  "fixedExample": "/reference/examples/rectangle-set-compose.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."
  }
}