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Public evidence

math.combinatorics

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

11/11 calculation tests · Production surface contract 4/4

  • Golden tests 2 / 2
  • Boundary tests 3 / 3
  • Property tests 6 / 6
  • Production surface contract 4 / 4
    • }
  • Engine tested Yes
  • Source checked Yes
  • Artifact integrity PASS
  • Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
  • Semantic contract PASS
  • Evidence attested at 2026-09-16T06:44:24.203Z
  • Last production check 2026-09-16T06:44:24.203Z
  • Public / cache —
  • Origin —
  • Supplemental domain review Not performed
  • Named expert review Not performed
  • release artifacts aligned PASS
  • schema valid input executes PASS
  • engine success output validates schema PASS
  • schema rejects incomplete input PASS

Fingerprint sha256:7e6eeaa69cdb1b2c70587975c2bc20dae683842b8ac1fcb2070fd44859cda07e

Input schema sha256:71247776818687a0fdf6f5a6ed18e38562fab8d1efc11b8e7cec5f97da15a36f · Output schema sha256:8e8ef711c388ceb0caa8b907c885e03f9580cd2e0f3530f4e1d0578e114eb27b · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool
combinatorics
Engine
combinatorics
Engine build
2026-09-16
Evidence core
2026-09-16T14:30:31.968Z
Rendered
2026-09-16T14:39:28.357Z
Last reviewed
—

Assumptions

  • Integers 0 ≤ k ≤ n ≤ 1000
  • Not factorial n!
  • Not multinomial and not with-replacement

Limitations

  • Not the factorial product page — use /calc/math/factorial for n!
  • Not multinomial coefficients and not with-replacement selections
  • Domain 0 ≤ k ≤ n ≤ 1000
  • k > n → INVALID_INPUT
  • unknown mode → INVALID_MODE

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

Published checks

Golden, boundary, and property cases included in this evidence build.

IDKindStatusDetail
golden-ncrgoldenpassExpected value=120 · mode=combination · Actual n=10 · value=120 · k=3 · mode=combination · symbol=C(10,3) · formula=C(n,k) = n! / (k!(n−k)!) · exact=120 · digits=3
golden-nprgoldenpassExpected value=720 · mode=permutation · Actual n=10 · value=720 · k=3 · mode=permutation · symbol=P(10,3) · formula=P(n,k) = n! / (n−k)! · exact=720 · digits=3
boundary-k-gt-nboundarypassExpected INVALID_INPUT · Actual INVALID_INPUT
boundary-combo-missingboundarypassExpected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
boundary-combo-modeboundarypassExpected INVALID_MODE · Actual INVALID_MODE
property-c-10-3propertypassC(10,3)=120
property-p-10-3propertypassP(10,3)=720
property-p-c-kpropertypassP(n,k)=C(n,k)·k!
property-c-sympropertypassC(n,k)=C(n,n−k)
property-c-zeropropertypassC(n,0)=1
property-p-nnpropertypassP(n,n)=n!