Public evidence

math.multiplication

Machine-checked verification for calculation version 1.0.3 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.0.3 · engine_tested · 15/15 tests. It is not the current published claim. Current evidence is 1.0.4 (15/15 tests) · latest.

CVP status

product or long mode; shared exact path; long steps independently reconstructed

Declared partition coverage: PASS · 5/5 declared partitions (product, long, long-grid, digit-bound, invalid-domain)
Versions: Calculation 1.0.3 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 6/6 property · digest 7a9319794cf7

Verification

Legacy regression suite: 15/15 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (15/15 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 2026-09-16.sources-no-wolfram. Calculation version 1.0.3. CVP 1.0.0-proposed. 12/12 golden · 5/5 CVP boundary · 4/4 invalid · 6/6 property · 2/2 metamorphic · 2/2 round-trip · 3/3 cross-interface · 4/4 CVP contract. digest 7a9319794cf7. Exact decimal-string identity (productStr) vs O2 mantissa×BigInt dual-checked against per-digit BigInt partials. Long vectors also require IUT work to contain those partials, or LONG_GRID_TRUNCATED at 25 digits. 48 significant digits per factor; 49-digit factors are rejected. This is not a whole-domain proof beyond the published vectors.

Golden (oracle-backed) 12 / 12
CVP boundary 5 / 5
Invalid input 4 / 4
Property 6 / 6
Metamorphic 2 / 2
Round-trip 2 / 2
Cross-interface 3 / 3
CVP contract 4 / 4
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 sha256:390204c17741107554921e0df97b92e39c1abeb92f6fc6d12aabcea1757958a9

Input schema sha256:694d72a0edef2b5a16d886a9b9d3aab856f17118d177c4fbb72bc3648a508d20 · Output schema sha256:82034e8d4b53198a999d386a7775a13a278e82762b93bfbfa317f5e7a1a11ae9 · 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: multiplication
Engine: multiplication
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-22T03:01:50.154Z
Last reviewed: —

Assumptions

Real decimal inputs parsed as exact decimal strings (integer mantissa × 10^−scale), not binary floating-point.
Product mode and Long multiplication mode use the same exact mantissa multiplication; Long adds partial-product steps.

Limitations

Missing a or b → INVALID_INPUT
Product and long modes share exact decimal mantissa × BigInt arithmetic
Very wide long grids may set LONG_GRID_TRUNCATED

Sources

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

CalculatorX mathematical conventions — Exact decimal place-count multiplication
Supports: Long-multiplication algorithm with partial products; exact decimal mantissa × BigInt; sign rules for negatives.
Margaret Stevens — The Maths Workbook (University of Oxford) — Chapter 1, §1: Algebraic Expressions and Fractions; §3: Equations
Supports: Algebraic addition/subtraction, multiplication/division, distributive rules, equivalent fractions, common denominators and reciprocals. Ratios are interpreted as quotients. Equality of ratios with nonzero denominators permits cross multiplication, and solving a proportion uses the chapter’s equation transformations. A zero divisor is excluded; integer quotient/remainder uses the separately cited Euclidean-division reference. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.

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.