{ "id": "decimal-distribution-summarize", "name": "Summarize exact decimal observations", "description": "Compute exact reduced-rational descriptive statistics and R type-7 quantiles from supplied decimal strings. Explicit null/error-or-omit policy, empty and singleton results, exact population/sample variance. No square roots, weighting, units, uncertainty or population inference.", "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": [ "Compute exact descriptive mean, variance, median and R7 percentiles from supplied decimal measurements", "Summarize decimal observations with explicit missing-value omission evidence" ], "whenToUse": [ "Compute exact descriptive mean, variance, median and R7 percentiles from supplied decimal measurements", "Summarize decimal observations with explicit missing-value omission evidence" ], "whenNotToUse": [ "Significance testing, confidence intervals, population estimates, verified measurements, standard deviation or automatic missing-value imputation", "Network calls, external actions, supplied-evidence authenticity or factual correctness certification" ], "capabilities": [ "Exact decimal strings up to 24 integer and 18 fraction digits, reduced rational results", "R type-7 interpolation only; probability order retained and numerical duplicates reject", "Missing indexes explicit; empty observations return zero sum and null other statistics", "Networkless bounded computation; advisoryOnly=true; externalRequests=0" ], "limits": { "inputBytes": 100000, "outputBytes": 400000, "jsonNodes": 12000, "depth": 20, "values": 1000, "quantiles": 21, "decimalIntegerDigits": 24, "decimalFractionDigits": 18, "rationalDigits": 2048, "arithmeticWorkSteps": 100000, "quantileMethod": "R7" }, "errorCodes": [ "INPUT_LIMIT", "OUTPUT_LIMIT", "COMPLEXITY_LIMIT", "INVALID_NUMBER", "INVALID_UNICODE", "UNSAFE_KEY", "MISSING_VALUE", "INVALID_PROBABILITY", "DUPLICATE_PROBABILITY", "NUMERIC_COMPLEXITY" ], "related": [ "localized-number-parse", "records-aggregate", "numeric-rounding-check" ], "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": "decimal-distribution-summarize", "operation.category": "data-assurance", "limit.httpRequestBytes": 131072, "limit.requestBytes": 100000, "limit.responseBytes": 524288, "limit.resultBytes": 400000, "limit.jsonDepth": 20, "limit.jsonNodes": 12000, "decimalSummary.profile": "exact-decimal-r7-summary-v1", "decimalSummary.maxValues": 1000, "decimalSummary.maxQuantiles": 21, "decimalSummary.maxIntegerDigits": 24, "decimalSummary.maxFractionDigits": 18, "decimalSummary.maxRationalDigits": 2048, "decimalSummary.maxWorkSteps": 100000, "decimalSummary.quantileMethod": "R7", "decimalSummary.missingnessExplicit": true, "decimalSummary.binaryFloatArithmetic": false, "decimalSummary.standardDeviation": false, "decimalSummary.populationInference": false, "decimalSummary.measurementValidityVerified": false, "input.values.maxItems": 1000, "input.quantiles.maxItems": 21 }, "unknownPolicy": "Undeclared requirements are unknown, never compatible. Matching declared facts does not establish semantic fit or input validity.", "preflight": "/preflight" }, "documentation": "/reference/tools/decimal-distribution-summarize.md", "serviceContract": "/reference/services/decimal-distribution-summarize.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/decimal-distribution-summarize", "mpp": "/v1/mpp/decimal-distribution-summarize" }, "inputSchema": { "$schema": "https://json-schema.org/draft/2020-12/schema", "type": "object", "properties": { "values": { "maxItems": 1000, "type": "array", "items": { "anyOf": [ { "type": "string", "maxLength": 44, "pattern": "^-?(?:0|[1-9]\\d{0,23})(?:\\.\\d{1,18})?$" }, { "type": "null" } ] } }, "missing": { "type": "string", "enum": [ "error", "omit" ] }, "quantiles": { "maxItems": 21, "type": "array", "items": { "type": "string", "maxLength": 43, "pattern": "^(?:0|[1-9]\\d{0,23})(?:\\.\\d{1,18})?$" } } }, "required": [ "values", "missing", "quantiles" ], "additionalProperties": false }, "outputSchema": { "type": "object", "required": [ "operation", "version", "result", "provenance" ], "properties": { "operation": { "const": "decimal-distribution-summarize", "type": "string" }, "version": { "const": "0.29.0", "type": "string" }, "result": { "$schema": "https://json-schema.org/draft/2020-12/schema", "type": "object", "properties": { "advisoryOnly": { "type": "boolean", "const": true }, "externalRequests": { "type": "number", "const": 0 }, "profile": { "type": "string", "const": "exact-decimal-r7-summary-v1" }, "status": { "type": "string", "enum": [ "summarized", "empty" ] }, "inputCount": { "type": "integer", "minimum": 0, "maximum": 9007199254740991 }, "observedCount": { "type": "integer", "minimum": 0, "maximum": 9007199254740991 }, "missingCount": { "type": "integer", "minimum": 0, "maximum": 9007199254740991 }, "omittedIndexes": { "maxItems": 1000, "type": "array", "items": { "type": "integer", "minimum": 0, "maximum": 9007199254740991 } }, "sum": { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, "min": { "anyOf": [ { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, { "type": "null" } ] }, "max": { "anyOf": [ { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, { "type": "null" } ] }, "mean": { "anyOf": [ { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, { "type": "null" } ] }, "median": { "anyOf": [ { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, { "type": "null" } ] }, "populationVariance": { "anyOf": [ { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, { "type": "null" } ] }, "sampleVariance": { "anyOf": [ { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, { "type": "null" } ] }, "quantiles": { "maxItems": 21, "type": "array", "items": { "type": "object", "properties": { "probability": { "type": "string", "maxLength": 43 }, "value": { "anyOf": [ { "type": "object", "properties": { "numerator": { "type": "string", "maxLength": 2049, "pattern": "^-?(?:0|[1-9]\\d*)$" }, "denominator": { "type": "string", "maxLength": 2048, "pattern": "^[1-9]\\d*$" } }, "required": [ "numerator", "denominator" ], "additionalProperties": false }, { "type": "null" } ] } }, "required": [ "probability", "value" ], "additionalProperties": false } }, "quantileMethod": { "type": "string", "const": "R7" }, "populationInference": { "type": "boolean", "const": false } }, "required": [ "advisoryOnly", "externalRequests", "profile", "status", "inputCount", "observedCount", "missingCount", "omittedIndexes", "sum", "min", "max", "mean", "median", "populationVariance", "sampleVariance", "quantiles", "quantileMethod", "populationInference" ], "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": { "values": [ "1.2", "2.4", "4.8", "7.2", null ], "missing": "omit", "quantiles": [ "0.25" ] }, "exampleResponse": { "operation": "decimal-distribution-summarize", "version": "0.29.0", "result": { "advisoryOnly": true, "externalRequests": 0, "profile": "exact-decimal-r7-summary-v1", "status": "summarized", "inputCount": 5, "observedCount": 4, "missingCount": 1, "omittedIndexes": [ 4 ], "sum": { "numerator": "78", "denominator": "5" }, "min": { "numerator": "6", "denominator": "5" }, "max": { "numerator": "36", "denominator": "5" }, "mean": { "numerator": "39", "denominator": "10" }, "median": { "numerator": "18", "denominator": "5" }, "populationVariance": { "numerator": "531", "denominator": "100" }, "sampleVariance": { "numerator": "177", "denominator": "25" }, "quantiles": [ { "probability": "0.25", "value": { "numerator": "21", "denominator": "10" } } ], "quantileMethod": "R7", "populationInference": false }, "provenance": { "inputSha256": "ba43b753b426000bc85f40d002986e7142da63e0e6543574b4175efdf716f060", "outputSha256": "446f17493b36b940a6b3bd24349ac063e1915aafda0117a8c72a76aea9460984", "deterministic": true, "externalRequests": 0 } }, "requiredHeaders": { "Content-Type": "application/json", "Idempotency-Key": "random 16–128 character operation identifier" }, "fixedExample": "/reference/examples/decimal-distribution-summarize.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." } }