{
  "id": "interval-analyze",
  "name": "Interval coverage and overlaps",
  "description": "Analyze up to 300 integer half-open intervals inside an explicit window: clipped union, gaps, covered/multiply-covered duration, concurrency segments and overlap-pair evidence. Touching endpoints do not overlap. No calendar access, reservations or scheduling actions.",
  "category": "data-assurance",
  "priceUsd": "0.005",
  "pricingStatus": "proposed-unverified",
  "pricing": {
    "unit": "one successful operation call",
    "proposedNominalUsd": "0.005",
    "sixDecimalTokenBaseUnits": "5000",
    "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": [
    "calculate interval coverage union gaps overlaps and concurrency",
    "inspect execution windows for overlaps and uncovered time",
    "find coverage gaps in supplied numeric ranges"
  ],
  "whenToUse": [
    "calculate interval coverage union gaps overlaps and concurrency",
    "inspect execution windows for overlaps and uncovered time",
    "find coverage gaps in supplied numeric ranges"
  ],
  "whenNotToUse": [
    "Book meetings mutate calendars or schedule execution",
    "Interpret timezone recurrences or continuous noninteger geometry"
  ],
  "capabilities": [
    "half-open interval union",
    "window clipping and gap analysis",
    "maximum concurrency",
    "complete overlap counts with bounded evidence"
  ],
  "related": [
    "time-series-inspect",
    "workflow-dag-analyze"
  ],
  "limits": {
    "inputBytes": 100000,
    "outputBytes": 400000,
    "jsonNodes": 12000,
    "depth": 20,
    "evidence": 200,
    "keyWorkBytes": 3000000,
    "matchingSteps": 2000000,
    "intervals": 300,
    "endpointAbsoluteMaximum": 1000000000000
  },
  "errorCodes": [
    "INPUT_LIMIT",
    "OUTPUT_LIMIT",
    "COMPLEXITY_LIMIT",
    "UNSAFE_KEY",
    "INVALID_NUMBER",
    "INVALID_POINTER",
    "DUPLICATE_ID",
    "DUPLICATE_FIELD",
    "INVALID_RULE",
    "KEY_WORK_LIMIT",
    "LABEL_LIMIT",
    "UNJUDGED_DOCUMENT",
    "INVALID_SPAN",
    "DUPLICATE_SPAN",
    "INVALID_UNICODE",
    "MATCHING_LIMIT",
    "INVALID_CADENCE",
    "INVALID_INTERVAL",
    "NUMERIC_OVERFLOW"
  ],
  "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": "interval-analyze",
      "operation.category": "data-assurance",
      "limit.httpRequestBytes": 131072,
      "limit.requestBytes": 100000,
      "limit.responseBytes": 524288,
      "limit.resultBytes": 400000,
      "limit.jsonDepth": 20,
      "limit.jsonNodes": 12000,
      "input.intervals.maxItems": 300,
      "input.unit.maxLength": 40,
      "input.unit.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/interval-analyze.md",
  "serviceContract": "/reference/services/interval-analyze.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/interval-analyze",
    "mpp": "/v1/mpp/interval-analyze"
  },
  "inputSchema": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "window": {
        "type": "object",
        "properties": {
          "start": {
            "type": "integer",
            "minimum": -1000000000000,
            "maximum": 1000000000000
          },
          "end": {
            "type": "integer",
            "minimum": -1000000000000,
            "maximum": 1000000000000
          }
        },
        "required": [
          "start",
          "end"
        ],
        "additionalProperties": false
      },
      "intervals": {
        "maxItems": 300,
        "type": "array",
        "items": {
          "type": "object",
          "properties": {
            "start": {
              "type": "integer",
              "minimum": -1000000000000,
              "maximum": 1000000000000
            },
            "end": {
              "type": "integer",
              "minimum": -1000000000000,
              "maximum": 1000000000000
            },
            "id": {
              "type": "string",
              "minLength": 1,
              "maxLength": 80
            }
          },
          "required": [
            "start",
            "end",
            "id"
          ],
          "additionalProperties": false
        }
      },
      "unit": {
        "default": "units",
        "type": "string",
        "minLength": 1,
        "maxLength": 40
      }
    },
    "required": [
      "window",
      "intervals"
    ],
    "additionalProperties": false
  },
  "outputSchema": {
    "type": "object",
    "required": [
      "operation",
      "version",
      "result",
      "provenance"
    ],
    "properties": {
      "operation": {
        "const": "interval-analyze",
        "type": "string"
      },
      "version": {
        "const": "0.29.0",
        "type": "string"
      },
      "result": {
        "$schema": "https://json-schema.org/draft/2020-12/schema",
        "type": "object",
        "properties": {
          "profile": {
            "type": "string",
            "const": "half-open-intervals-v1"
          },
          "unit": {
            "type": "string"
          },
          "window": {
            "type": "object",
            "properties": {
              "start": {
                "type": "integer",
                "minimum": -1000000000000,
                "maximum": 1000000000000
              },
              "end": {
                "type": "integer",
                "minimum": -1000000000000,
                "maximum": 1000000000000
              }
            },
            "required": [
              "start",
              "end"
            ],
            "additionalProperties": false
          },
          "intervalCount": {
            "type": "integer",
            "minimum": 0,
            "maximum": 9007199254740991
          },
          "consideredCount": {
            "type": "integer",
            "minimum": 0,
            "maximum": 9007199254740991
          },
          "outsideWindowIds": {
            "type": "array",
            "items": {
              "type": "string"
            }
          },
          "clippedIds": {
            "type": "array",
            "items": {
              "type": "string"
            }
          },
          "coveredDuration": {
            "type": "integer",
            "minimum": 0,
            "maximum": 9007199254740991
          },
          "uncoveredDuration": {
            "type": "integer",
            "minimum": 0,
            "maximum": 9007199254740991
          },
          "multiplyCoveredDuration": {
            "type": "integer",
            "minimum": 0,
            "maximum": 9007199254740991
          },
          "maximumConcurrency": {
            "type": "integer",
            "minimum": 0,
            "maximum": 9007199254740991
          },
          "coverage": {
            "type": "array",
            "items": {
              "type": "object",
              "properties": {
                "start": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                },
                "end": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                },
                "activeCount": {
                  "type": "integer",
                  "minimum": 0,
                  "maximum": 9007199254740991
                }
              },
              "required": [
                "start",
                "end",
                "activeCount"
              ],
              "additionalProperties": false
            }
          },
          "union": {
            "type": "array",
            "items": {
              "type": "object",
              "properties": {
                "start": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                },
                "end": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                }
              },
              "required": [
                "start",
                "end"
              ],
              "additionalProperties": false
            }
          },
          "gaps": {
            "type": "array",
            "items": {
              "type": "object",
              "properties": {
                "start": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                },
                "end": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                }
              },
              "required": [
                "start",
                "end"
              ],
              "additionalProperties": false
            }
          },
          "overlappingPairCount": {
            "type": "integer",
            "minimum": 0,
            "maximum": 9007199254740991
          },
          "overlappingPairs": {
            "type": "array",
            "items": {
              "type": "object",
              "properties": {
                "start": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                },
                "end": {
                  "type": "integer",
                  "minimum": -1000000000000,
                  "maximum": 1000000000000
                },
                "leftId": {
                  "type": "string"
                },
                "rightId": {
                  "type": "string"
                }
              },
              "required": [
                "start",
                "end",
                "leftId",
                "rightId"
              ],
              "additionalProperties": false
            }
          },
          "overlappingPairsTruncated": {
            "type": "boolean"
          },
          "conventions": {
            "type": "array",
            "items": {
              "type": "string"
            }
          }
        },
        "required": [
          "profile",
          "unit",
          "window",
          "intervalCount",
          "consideredCount",
          "outsideWindowIds",
          "clippedIds",
          "coveredDuration",
          "uncoveredDuration",
          "multiplyCoveredDuration",
          "maximumConcurrency",
          "coverage",
          "union",
          "gaps",
          "overlappingPairCount",
          "overlappingPairs",
          "overlappingPairsTruncated",
          "conventions"
        ],
        "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": {
    "window": {
      "start": 0,
      "end": 20
    },
    "intervals": [
      {
        "id": "a",
        "start": 2,
        "end": 8
      },
      {
        "id": "b",
        "start": 6,
        "end": 12
      },
      {
        "id": "c",
        "start": 15,
        "end": 25
      }
    ],
    "unit": "seconds"
  },
  "exampleResponse": {
    "operation": "interval-analyze",
    "version": "0.29.0",
    "result": {
      "profile": "half-open-intervals-v1",
      "unit": "seconds",
      "window": {
        "start": 0,
        "end": 20
      },
      "intervalCount": 3,
      "consideredCount": 3,
      "outsideWindowIds": [],
      "clippedIds": [
        "c"
      ],
      "coveredDuration": 15,
      "uncoveredDuration": 5,
      "multiplyCoveredDuration": 2,
      "maximumConcurrency": 2,
      "coverage": [
        {
          "start": 0,
          "end": 2,
          "activeCount": 0
        },
        {
          "start": 2,
          "end": 6,
          "activeCount": 1
        },
        {
          "start": 6,
          "end": 8,
          "activeCount": 2
        },
        {
          "start": 8,
          "end": 12,
          "activeCount": 1
        },
        {
          "start": 12,
          "end": 15,
          "activeCount": 0
        },
        {
          "start": 15,
          "end": 20,
          "activeCount": 1
        }
      ],
      "union": [
        {
          "start": 2,
          "end": 12
        },
        {
          "start": 15,
          "end": 20
        }
      ],
      "gaps": [
        {
          "start": 0,
          "end": 2
        },
        {
          "start": 12,
          "end": 15
        }
      ],
      "overlappingPairCount": 1,
      "overlappingPairs": [
        {
          "start": 6,
          "end": 8,
          "leftId": "a",
          "rightId": "b"
        }
      ],
      "overlappingPairsTruncated": false,
      "conventions": [
        "All intervals are half-open [start,end); touching endpoints do not overlap. Results are clipped to the explicit window.",
        "Coverage segments represent active counts, not interval identity. Pair counts include every overlap even when retained evidence is truncated. Units are caller-declared; no scheduling action is performed."
      ]
    },
    "provenance": {
      "inputSha256": "14a28f54ff2cc9b8b24efc58e227f8ab3e1961948d1cac7ce9eb0d6c05d52f16",
      "outputSha256": "294ba7cd239f7eba59845ab765a99c804049f5f7c1e97af230ca8a65b97e8568",
      "deterministic": true,
      "externalRequests": 0
    }
  },
  "requiredHeaders": {
    "Content-Type": "application/json",
    "Idempotency-Key": "random 16–128 character operation identifier"
  },
  "fixedExample": "/reference/examples/interval-analyze.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."
  }
}