Public evidence

math.fractions

Machine-checked verification for calculation version 1.0.6 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.0.6 · engine_tested · 32/32 tests. It is not the current published claim. Current evidence is 1.0.8 (32/32 tests) · latest.

CVP status

O2 BigInt gold covers operate (+/−/×/÷) and simplify only. Fraction integer inputs and every arithmetic intermediate must be safe integers (|x| ≤ 2^53−1); overflow returns VALUE_OUT_OF_RANGE. to-dec and from-dec have engine regression coverage, not O2 mode verification.

Declared partition coverage: PASS · 6/6 declared partitions (operate:add, operate:subtract, operate:multiply, operate:divide, simplify, invalid-domain)
Versions: Calculation 1.0.6 · CVP protocol 1.0.0-proposed · Evidence 2026-09-30.safe-integer-scope
Verification revision: 2026-09-30.safe-integer-scope · 2/2 property · digest b2e72767e4a4

Verification

Legacy regression suite: 32/32 calculation tests · Production surface contract 5/5

Three distinct suites: educational examples on the calculator page, this legacy regression count (32/32 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 1.0.8 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 2026-09-30.safe-integer-scope. Calculation version 1.0.6. CVP 1.0.0-proposed. 6/6 golden · 8/8 CVP boundary · 8/8 invalid · 2/2 property · 1/1 metamorphic · 1/1 round-trip · 7/7 cross-interface · 5/5 CVP contract. digest b2e72767e4a4.

Golden (oracle-backed) 6 / 6
CVP boundary 8 / 8
Invalid input 8 / 8
Property 2 / 2
Metamorphic 1 / 1
Round-trip 1 / 1
Cross-interface 7 / 7
CVP contract 5 / 5
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Verified scope operate (+/−/×/÷) and simplify
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:c22300e344070a95a3c8831f8dc26c0c9adbc88a96cb7aaf50303d2755e30b34

Input schema sha256:6a1a9267461a8f953ff6f8289ffbd2ad64525cc914f53be9132b15f325487864 · Output schema sha256:0c0a783a6f09275e7cb36fc533c12637800f7c0383df922c28c7a0cece5c8b31 · 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: fractions
Engine: fractions
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-20T10:42:53.057Z
Last reviewed: —

Assumptions

Fraction inputs and every arithmetic intermediate must be safe integers (absolute value at most 2^53−1); otherwise VALUE_OUT_OF_RANGE.
From decimal uses binary64 conversion and is engine tested, outside the current O2 CVP verified scope.
Results reduced by GCF; signs normalized onto the numerator.

Limitations

Integer numerators and denominators only (optional mixed-number whole)
Denominator 0 → DENOMINATOR_MUST_BE_NONZERO
Division by 0/n → DIVISION_BY_ZERO
Add/subtract use LCD = LCM(b, d); (ad ± bc)/bd is an equivalent check only
Negative sign is normalized onto the numerator after reduction
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.

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.

Methods

Algorithms this engine uses. Not external references.

LCD / LCM addition and subtraction
Cross-product identity (equivalent to LCD, used as a check)
GCF reduction
Reciprocal (keep–change–flip) division

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.