Public evidence

math.ratio

Machine-checked verification for calculation version 1.0.2 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.0.2 · engine_tested · 26/26 tests. It is not the current published claim. Current evidence is 1.0.3 (26/26 tests) · latest.

CVP status

Declared CVP coverage is all six published modes (simplify, proportion, scale, split, compare, convert), including A:B:C where those modes support it. Integer, terminating-decimal, and simple a/b terms.

Declared partition coverage: PASS · 8/8 declared partitions (simplify, proportion, scale, split, compare, convert, three-term, 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 · 7/7 property · digest e32c91d652f9

Verification

Legacy regression suite: 26/26 calculation tests · Production surface contract 10/10

Three distinct suites: educational examples on the calculator page, this legacy regression count (26/26 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 2026-09-16.sources-no-wolfram. Calculation version 1.0.2. CVP 1.0.0-proposed. 13/13 golden · 7/7 CVP boundary · 7/7 invalid · 7/7 property · 2/2 metamorphic · 2/2 round-trip · 3/3 cross-interface · 8/8 CVP contract. digest e32c91d652f9. All six published Ratio modes (simplify, proportion, scale, split, compare, convert), including A:B:C where those modes support it. Independent O2 expected values; exact rational BigInt; Node is runtime host only.

Golden (oracle-backed) 13 / 13
CVP boundary 7 / 7
Invalid input 7 / 7
Property 7 / 7
Metamorphic 2 / 2
Round-trip 2 / 2
Cross-interface 3 / 3
CVP contract 8 / 8
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Verified scope all published modes
Assurance Core

release artifacts aligned PASS
schema output required declared PASS
schema valid input executes PASS
engine success output validates schema PASS
explanation formula n term PASS
explanation steps match result PASS
explanation inputs summary PASS
explanation calculation version PASS
explanation arity PASS
rest success payload validates schema PASS

Fingerprint sha256:dac908da70997d5d17219bced551bfbb3489d162043cbc082941e63da82008f4

Input schema sha256:f265bc76ddf4ac054863a56d32fe03592f46d7a183cf98ad39c180496f456d46 · Output schema sha256:a88be281f59641c093c0fb7b28328ac502a4d55a7cda009c4ab75bc5f195a1ca · 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: ratio
Engine: ratio
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-21T03:33:24.147Z
Last reviewed: —

Assumptions

Finite rationals: integers, terminating decimals, or simple fractions a/b.
Proportion denominators in A/B or C/D must be nonzero when used.
Simplify / proportion / compare allow negative terms. Split does not.

Limitations

Integers, terminating decimals, and simple a/b fractions only (no mixed numbers or scientific notation)
Each term ≤ 48 decimal digits
Simplify / proportion / compare allow negative terms
Split requires every term ≥ 0 and Σ terms > 0 → SPLIT_NEGATIVE_TERM / SPLIT_ZERO_SUM
All-zero simplify → ALL_ZERO
Proportion needs exactly one blank among A,B,C,D → PROPORTION_ONE_BLANK
Expert review pending — L1 engine-tested / source-checked

Sources

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

Encyclopedia of Mathematics — Greatest common divisor — Pairwise Euclidean GCF used after clearing denominators
Supports: Computation of the GCF of the integerized ratio terms after clearing denominators; multiple-term GCF is obtained iteratively (GCF(a,b,c)=GCF(GCF(a,b),c))
CalculatorX split convention — Nonnegative parts only
Supports: Split requires every term ≥ 0 and Σ terms > 0, so shares are nonnegative allocations of a total
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.