Public evidence

math.algebra.linear_equation

Machine-checked verification for calculation version 1.5.1 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

Six discovery entries share one bounded one-variable engine; no quadratic/system/CAS. Distinct exact boundaries rounding toonefloat reject.

Declared partition coverage: PASS · 7/7 declared partitions (invalid-domain, mode-solve, mode-inequality, mode-abs, mode-abs_inequality, mode-rational, mode-rational_inequality)
Versions: Calculation 1.5.1 · CVP protocol 1.0.0-proposed · Evidence 2026-10-28.meta-metrics-v2
Verification revision: 2026-10-28.meta-metrics-v2 · 1/1 property · digest f9b7ec60bdd7

Verification

Legacy regression suite: 18/18 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (18/18 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.

This calculator CURRENT · Public schema 1.5.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-28.meta-metrics-v2. Calculation version 1.5.1. CVP 1.0.0-proposed. 178/178 golden · 1/1 CVP boundary · 12/12 invalid · 1/1 property · 2/2 metamorphic · 178/178 cross-interface · 6/6 CVP contract. digest f9b7ec60bdd7. Listed independent full-pack vectors only; classification uses exact comparisons, no absolute epsilon.

Golden (oracle-backed) 178 / 178
CVP boundary 1 / 1
Invalid input 12 / 12
Property 1 / 1
Metamorphic 2 / 2
Cross-interface 178 / 178
CVP contract 6 / 6
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Verified scope all six published modes
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:e5ad5fe3a04a28643e352f33467a6aac49b10a08eccd42ddc3926881e0a9b8ab

Input schema sha256:586b391b4b6e11c37cd67ea08f5acd59bc31794624f7321a7116e97e5f76a0b1 · Output schema sha256:245ef5eaf7fe98c652db13600bf7e8203c50145057e7da4d90a1d1310e90d03b · 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: linear-equation
Engine: linear-equation
Engine build: 2026-10-27
Evidence core: 2026-10-27T06:31:51.020Z
Rendered: 2026-10-29T17:04:55.747Z
Last reviewed: —

Assumptions

Degree 1 only
Not quadratic

Limitations

One variable:linear equation/inequality,absolute equation/inequality,rational equation/inequality. Accepted coefficients are finite binary64; exact rational decisions use those rounded inputs, not arbitrary-precision raw decimals.
Strict decimal/scientific text up to512 characters; nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. a andrhs required,b defaults0; rational c,d default0 andcannot bothzero. Nonrational c/d are rhs aliases andmust agree. Unknown keys,conflicts,invalid modes/relations andexplicit blank fields reject.
Returned solution ranges preserve open/closed endpoints andexcluded poles. No epsilon zero/pole/root merging. Endpoints are rounded once tobinary64; overflow/underflow ordistinct exact boundaries collapsing toonebinary64 value reject explicitly. Exact arithmetic is bounded to16384 numerator/denominator bits.
178 independent Fraction predicate/open-cell references compare complete result packs. One-ULP numerical ceiling for listed vectors; current full serialized comparisons are strict. No whole-domain/cross-runtime guarantee. Display/native result pack remain separate.
Six discovery entries lock their documented mode exceptthe canonical page,which accepts all modes. Typing local;share/REST/MCP transmit data andmay enter logs. Real screen reader user-deferred.

Sources

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

ISO 80000-2:2019 Quantities and units — Mathematics
Supports: Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.
CRC Standard Mathematical Tables — linear equations, absolute value, and linear rational equations
Supports: x = (rhs − b)/a; |ax+b| = rhs has two roots when rhs > 0; (ax+b)/(cx+d) = rhs clears to a linear equation excluding the pole
Margaret Stevens — The Maths Workbook (University of Oxford) — Chapter 1, §§1 and 3: Algebraic Expressions and Equations Chapter 1, §5: Inequalities and Absolute Value Chapter 1, §5: Inequalities and Absolute Value Chapter 1, §§1 and 3: Algebraic Expressions and Equations
Supports: Algebraic fraction simplification and solving linear equations, including equations with parameters and rearranging formulas. A denominator must be nonzero; candidates introduced by clearing denominators must be checked in the original equation. Mathematical reference only; not implementation validation or an endorsement of CalculatorX. The piecewise definition of |x|, reversal of inequalities under a negative factor, and worked absolute-value equation and inequality solutions. The calculator applies these rules to its stated linear arguments and zero/negative right-hand-side cases. Mathematical reference only; not implementation validation or an endorsement of CalculatorX. The piecewise definition of |x|, reversal of inequalities under a negative factor, and worked absolute-value equation and inequality solutions. The calculator applies these rules to its stated linear arguments and zero/negative right-hand-side cases. Mathematical reference only; not implementation validation or an endorsement of CalculatorX. Algebraic fraction simplification and solving linear equations, including equations with parameters and rearranging formulas. A denominator must be nonzero; candidates introduced by clearing denominators must be checked in the original equation. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.
University of Oxford Mathematical Institute — Algebra — Linear/quadratic inequalities and sign of factors
Supports: Factoring polynomials and determining sign intervals, with explicit quadratic-inequality examples. For a rational inequality the calculator applies the same factor-sign rules to numerator and denominator separately and excludes denominator zeros; that rational extension is a derived application, not a claim that the page tests this solver. 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.