Public evidence

math.gcf

Machine-checked verification for calculation version 1.0.3 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

2–32 signed integers up to48 decimal digits; ignore zeros unless all zero; bounded work and complete output

Declared partition coverage: PASS · 8/8 declared partitions (gcf, zero, negative, beyond-safe-integer, multi-input-fold, method-unavailable, xcal, invalid-domain)
Versions: Calculation 1.0.3 · CVP protocol 1.0.0-proposed · Evidence 2026-10-21.gcf-complete-contract-v4
Verification revision: 2026-10-21.gcf-complete-contract-v4 · 3/3 property · digest 9af66f58265f

Verification

Legacy regression suite: 20/20 calculation tests · Production surface contract 6/6

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.

STALE · Build schema 1.0.3 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-21.gcf-complete-contract-v4. Calculation version 1.0.3. CVP 1.0.0-proposed. 10/10 golden · 7/7 CVP boundary · 5/5 invalid · 3/3 property · 1/1 metamorphic · 2/2 cross-interface · 5/5 cross-calculator · 6/6 CVP contract. digest 9af66f58265f.

Golden (oracle-backed) 10 / 10
CVP boundary 7 / 7
Invalid input 5 / 5
Property 3 / 3
Metamorphic 1 / 1
Cross-interface 2 / 2
Cross-calculator 5 / 5
CVP contract 6 / 6
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 output required declared PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS
rest success payload validates schema PASS

Fingerprint sha256:b5ca6c5034df2c9fba1a9ca8afe6cc0a9359c6812c6565236dda70cf5a8eec44

Input schema sha256:ce1ac2ed33e6c016b2012f7aa646efc00ad1121d9ffcb0aea9b01b3c250db6c9 · Output schema sha256:8cef94e42e0aa48e26d23b4c8fa246350b2a7245f87eb4934277534da34744f3 · 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: 2026-10-21
Evidence core: 2026-10-21T01:07:42.434Z
Rendered: 2026-10-21T06:31:01.613Z
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
At most32 integers; list text≤4096 characters, individual array strings≤128 characters
Aliases values/numbers/numsInput must normalize to the same ordered list; unknown fields rejected
Exactness refers to accepted integers. Nonzero raw JSON underflow and unsafe numeric integers are rejected.
Method agreement is an internal cross-check, not third-party certification.

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
MIT Mathematics for Computer Science — Chapter 8: Number Theory — Chapter 8, including sections 8.2–8.9 and problem 8.24
Supports: Divisibility, prime factorization, gcd and the Euclidean algorithm, lcm via prime exponents, division with remainder, modular congruence and multiplicative inverses. CalculatorX’s signed-remainder and zero-input policies are stated separately on the page. Mathematical reference only; not validation or endorsement of this implementation.

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)

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.