math.factorial

Three distinct suites: educational examples on the calculator page, this legacy regression count (24/24 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 1.0.4 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 2026-09-08.exact-integer-profile. Calculation version 1.0.2. CVP 1.0.0-proposed. 6/6 golden · 7/7 CVP boundary · 6/6 invalid · 19/19 property · 5/5 metamorphic · 23/23 O3 · 1/1 cross-interface · 1/1 CVP contract. digest b7065c58307c. Exact decimal-string identity vs Python math.factorial on the 23 published tabulated vectors (named 0,1,5,10,20,100,5000 plus 16 seeded n in 0–4999). 5000! is verified as the full 16,326-digit value and as SHA-256 of those ASCII digits. This is not a whole-domain proof beyond the published table.

• Golden (oracle-backed) 6 / 6
• CVP boundary 7 / 7
• Invalid input 6 / 6
• Property 19 / 19
• Metamorphic 5 / 5
• O3 independent oracle 23 / 23
• Cross-interface 1 / 1
• CVP contract 1 / 1
• 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
• rest success payload validates schema PASS

Fingerprint sha256:316d01876698831ff0c9b1d2d351d3c8c971e92e92f1898ee98f855297b07420

Input schema sha256:8d6705e6f951df49c2cf9d961827b9ee167172c12789649142077d31552f61dc · Output schema sha256:f041a1d2bd0b46c619498de4bd9adda7303f09e8f8fb1b5df8ba1f4695ca7f04 · 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.

Tool

factorial

Engine

factorial

Engine build

2026-10-14

Evidence core

2026-10-14T02:50:33.742Z

Rendered

2026-10-20T09:28:01.654Z

Last reviewed

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Assumptions

• n is an integer satisfying 0 ≤ n ≤ 5000.
• Ordinary (single) factorial only — not multifactorial and not the real Gamma function for non-integers.

Limitations

• Ordinary (single) factorial only — not multifactorial and not Γ(n+1) for non-integers
• Domain is 0 ≤ n ≤ 5000 (product/resource bound, not a mathematical bound)
• Missing n → MISSING_REQUIRED_INPUT
• Non-numeric or non-integer n → INVALID_NUMBER
• n < 0 → VALUE_MUST_BE_NON_NEGATIVE
• n > 5000 → VALUE_ABOVE_MAX