Exact integer rectangle set algebra
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.
data-assurance · Operation ID: rectangle-set-compose
Choose this operation when
- 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
Outside this profile
- 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
Exact release references
Static JSON contract · Markdown reference · Fixed example response
Complete input schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"type": "object",
"properties": {
"operation": {
"type": "string",
"enum": [
"union",
"intersection",
"difference",
"xor"
]
},
"a": {
"maxItems": 32,
"type": "array",
"items": {
"type": "array",
"prefixItems": [
{
"type": "string",
"maxLength": 14,
"pattern": "^(?:0|-?[1-9][0-9]*)$"
},
{
"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]*)$"
}
],
"items": false,
"minItems": 4,
"maxItems": 4
}
}
},
"required": [
"operation",
"a",
"b"
],
"additionalProperties": false
}
Complete output-envelope schema
{
"type": "object",
"required": [
"operation",
"version",
"result",
"provenance"
],
"properties": {
"operation": {
"const": "rectangle-set-compose",
"type": "string"
},
"version": {
"const": "0.29.0",
"type": "string"
},
"result": {
"$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
}
Fixed example
One accepted fixed example, not a custom-input trial. No operation runs when this static page is requested.
Example input
{
"operation": "difference",
"a": [
[
"0",
"0",
"6",
"4"
]
],
"b": [
[
"2",
"1",
"4",
"3"
]
]
}
Example response
{
"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
}
}
Bounds and precision
JavaScript IEEE-754 numbers; use strings for large integer IDs/exact decimals where the schema accepts strings. No lossless numeric parsing.
{
"global": {
"requestBytes": 131072,
"responseBytes": 524288,
"jsonDepth": 32,
"jsonNodes": 20000,
"requestsPerMinute": 60,
"paidAttemptsPerMinute": 20,
"idempotencyHours": 24
},
"operation": {
"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
}
}
Complete schemas, descriptions and cross-field validation may impose additional limits.
Proposed price and protocol definitions
{
"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."
}
Protocol definitions: x402, mpp. MPP uses Tempo charge. Paid MCP execution is unsupported. All runtime readiness is not evaluated in this build.
API path templates, not endpoints on this documentation host
{
"x402": "/v1/x402/rectangle-set-compose",
"mpp": "/v1/mpp/rectangle-set-compose"
}
Required headers
{
"Content-Type": "application/json",
"Idempotency-Key": "random 16–128 character operation identifier"
}
Actual SDK challenge amount, asset, network, recipient and wallet costs must pass independent authorization. Preserve identical key, body, protocol and credential on retries; on PAYMENT_UNCERTAIN stop and reconcile.
Execution profile and provider conditions
{
"deterministic": true,
"externalRequests": 0,
"maxExternalRequests": 0,
"resultSnapshotPersisted": false,
"fixedExampleIsIllustrativeSnapshot": false,
"requiresPayment": true,
"supportsMcpExecution": false
}
Deterministic supplied-input operation with no external requests or stored request/result bodies. Payment infrastructure retains payment metadata and hashes.
Failure handling
- HTTP 400: Malformed JSON, missing/invalid idempotency key, or payment identifier mismatch Correct the request before payment
- HTTP 402: Payment challenge or rejected payment Use official protocol SDK; inspect payment outcome before another payment
- HTTP 409: Idempotency conflict, duplicate proof, or PAYMENT_UNCERTAIN Keep original key, body, and proof; reconcile uncertainty with operator; never blindly repay
- HTTP 413: Input or generated output too large Reduce input; no payment attempted for validation failure
- HTTP 415: Unsupported media type or compression Send uncompressed application/json
- HTTP 422: Schema or service-specific semantic validation failure Correct input using returned error code; no payment attempted
- HTTP 429: Request/payment-attempt rate exceeded Wait for rate limit window; preserve existing payment identity
- HTTP 503: Payment configuration/provider/state unavailable, or live DNS preparation failed before settlement Check readiness; DNS preparation failures may retry the identical key/body/credential only; uncertainty requires reconciliation
Declared requirements
Before any paid call, refresh the live operation contract and POST the complete bounded budgeted plan to the separate API's /preflight. Unknown requirements block selection; compatible preflight is not permission to spend.