Summarize exact decimal observations
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.
data-assurance · Operation ID: decimal-distribution-summarize
Choose this operation when
- Compute exact descriptive mean, variance, median and R7 percentiles from supplied decimal measurements
- Summarize decimal observations with explicit missing-value omission evidence
Outside this profile
- 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
Exact release references
Static JSON contract · Markdown reference · Fixed example response
Complete input schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"type": "object",
"properties": {
"values": {
"maxItems": 1000,
"type": "array",
"items": {
"anyOf": [
{
"type": "string",
"maxLength": 44,
"pattern": "^-?(?:0|[1-9]\\d{0,23})(?:\\.\\d{1,18})?$"
},
{
"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})?$"
}
}
},
"required": [
"values",
"missing",
"quantiles"
],
"additionalProperties": false
}
Complete output-envelope schema
{
"type": "object",
"required": [
"operation",
"version",
"result",
"provenance"
],
"properties": {
"operation": {
"const": "decimal-distribution-summarize",
"type": "string"
},
"version": {
"const": "0.29.0",
"type": "string"
},
"result": {
"$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
}
Fixed example
One accepted fixed example, not a custom-input trial. No operation runs when this static page is requested.
Example input
{
"values": [
"1.2",
"2.4",
"4.8",
"7.2",
null
],
"missing": "omit",
"quantiles": [
"0.25"
]
}
Example response
{
"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
}
}
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": 400000,
"jsonNodes": 12000,
"depth": 20,
"values": 1000,
"quantiles": 21,
"decimalIntegerDigits": 24,
"decimalFractionDigits": 18,
"rationalDigits": 2048,
"arithmeticWorkSteps": 100000,
"quantileMethod": "R7"
}
}
Complete schemas, descriptions and cross-field validation may impose additional limits.
Proposed price and protocol definitions
{
"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."
}
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/decimal-distribution-summarize",
"mpp": "/v1/mpp/decimal-distribution-summarize"
}
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.