Public evidence

math.gcf

Machine-checked verification for calculation version 1.0.2 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· ≥2 integers; ignore zeros unless all zero · Protocol · Schema · Production report

Declared partition coverage: PASS · 8/8 declared partitions (gcf, zero, negative, beyond-safe-integer, multi-input-fold, method-unavailable, xcal, invalid-domain)
Versions: Calculation 1.0.2 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 3/3 property · digest 2f7e2bf9bb70

Verification

Legacy regression suite: 20/20 calculation tests · Production surface contract 3/3

Three distinct suites: educational examples on the calculator page, this legacy regression count (20/20 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.2 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-16.sources-no-wolfram. Calculation version 1.0.2. CVP 1.0.0-proposed. 4/4 golden · 7/7 CVP boundary · 5/5 invalid · 3/3 property · 1/1 metamorphic · 1/1 cross-interface · 5/5 cross-calculator · 3/3 CVP contract. digest 2f7e2bf9bb70.

Golden (oracle-backed) 4 / 4
CVP boundary 7 / 7
Invalid input 5 / 5
Property 3 / 3
Metamorphic 1 / 1
Cross-interface 1 / 1
Cross-calculator 5 / 5
CVP contract 3 / 3
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Assurance Core

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS

Fingerprint sha256:ce4c8fd3816846a3947cf60cc5a029f9ac4466c2dbe18ebc7381d0b2803029fc

Input schema sha256:937a6e502dea5e3c5dfc1ddc415dfe74551baf9c69172984c2beceac52db1c58 · Output schema sha256:0197666ba550d0fd10d924e139641734a798a04db1fcf2a2b5f25113ce68d993 · 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: gcf
Engine: gcf
Engine build: 2026-09-16
Evidence core: 2026-09-16T06:41:00.884Z
Rendered: 2026-09-16T22:03:43.771Z
Last reviewed: —

Assumptions

Integer inputs; negatives treated by absolute value.
Zeros are ignored unless every input is 0.
GCF of a set of all zeros is undefined.

Limitations

Integers only; negatives treated by absolute value
Each integer ≤ 48 decimal digits (product bound, not a mathematical bound)
Zeros are ignored unless every input is 0 (then UNDEFINED)
Need at least two numbers → NEED_TWO_NUMBERS
Non-integers → INVALID_NUMBER
Integers beyond MAX_SAFE_INTEGER must be decimal strings in JSON

Sources

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

Encyclopedia of Mathematics — Greatest common divisor — Definition; pairwise fold; prime-factor form
Supports: GCF of n integers exists when not all are zero; (a₁,…,aₙ,aₙ₊₁)=((a₁,…,aₙ),aₙ₊₁); shared-prime min exponents
Encyclopedia of Mathematics — Euclidean algorithm — Remainder recurrence GCF(a,b)=GCF(b, a mod b)
Supports: Binary Euclidean primitive used inside the pairwise fold
CalculatorX integer convention — Absolute value; zero-set; 48-digit BigInt domain
Supports: Negatives by |n|; ignore zeros unless the whole set is 0; exact BigInt with a product digit cap

Methods

Algorithms this engine uses. Not external references.

Pairwise Euclidean fold (canonical engine)
Prime-factor GCF (cross-check when every |n| ≤ 1,000,000)
Factor-list GCF (cross-check when every |n| ≤ 10,000)

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`triple`	golden	pass	Expected value=4 · exact=4 · Actual value=4 · exact=4 · count=3 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`pair`	golden	pass	Expected value=9 · Actual value=9 · exact=9 · count=2 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`with-zero`	golden	pass	Expected value=5 · Actual value=5 · exact=5 · count=2 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`zero-zero-5`	golden	pass	Expected value=5 · Actual value=5 · exact=5 · count=3 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`bigint-unsafe`	golden	pass	Expected value=3 · Actual value=3 · exact=3 · count=2 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`numsInput`	golden	pass	Expected value=4 · Actual value=4 · exact=4 · count=3 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`boundary-all-zero-pair`	boundary	pass	Expected UNDEFINED · Actual UNDEFINED
`boundary-all-zero-triple`	boundary	pass	Expected UNDEFINED · Actual UNDEFINED
`boundary-one-number`	boundary	pass	Expected NEED_TWO_NUMBERS · Actual NEED_TWO_NUMBERS
`boundary-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-non-integer`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`boundary-alias-numsInput`	boundary	pass	Expected value=4 · exact=4 · Actual value=4 · exact=4 · count=3 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`boundary-bigint-unsafe`	boundary	pass	Expected value=3 · Actual value=3 · exact=3 · count=2 · formula=GCF(a,b,c,…) = GCF(GCF(a,b),c,…) · binary_formula=GCF(a,b)=GCF(b, a mod b) · max_digits=48
`property-commutative-fold`	property	pass	GCF(8,12,20) = GCF(20,12,8) = 4
`property-three-methods-agree`	property	pass	factor, prime, and Euclidean all return 4
`property-ignore-zeros`	property	pass	GCF(0,0,12,20) = GCF(12,20)
`property-gcf-k-0`	property	pass	GCF(-48,0)=48
`property-bigint-beyond-safe-integer`	property	pass	GCF(9007199254740993, 3) = 3 (BigInt; IEEE-754 Number would round)
`property-pairwise-associative`	property	pass	GCF(GCF(48,18),30) = GCF(48,18,30)
`property-divides-each`	property	pass	4 divides 8, 12, and 20