Public evidence

math.quadratic

Machine-checked verification for calculation version 1.1.1 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest Reproduce MCP Review policy

CVP status

Declared partitions are two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain — plus inequality-two-roots, inequality-repeated, inequality-no-real-roots, inequality-rhs, inequality-fractions; not a claim that every quadratic is covered. Near-double-root, large-scale, and cancellation are numerical-boundary partitions and are in the O3 tabulated ULP claim.

Declared partition coverage: PASS · 14/14 declared partitions (inequality-two-roots, inequality-repeated, inequality-no-real-roots, inequality-rhs, inequality-fractions, two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain)
Versions: Calculation 1.1.1 · CVP protocol 1.0.0-proposed · Evidence 2026-10-13.quadratic-interface-replay
Verification revision: 2026-10-13.quadratic-interface-replay · 5/5 property · digest 4dddb83bf6df

Verification

Legacy regression suite: 9/9 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (9/9 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 1.1.1 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 2026-10-13.quadratic-interface-replay. Calculation version 1.1.1. CVP 1.0.0-proposed. 40/40 golden · 3/3 CVP boundary · 10/10 invalid · 5/5 property · 1/1 metamorphic · 12/12 O3 · 11/11 cross-interface · 6/6 CVP contract. digest 4dddb83bf6df. ≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, tiny-complex, tiny-real, tiny-scale, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a).

Golden (oracle-backed) 40 / 40
CVP boundary 3 / 3
Invalid input 10 / 10
Property 5 / 5
Metamorphic 1 / 1
O3 high-precision 12 / 12
Cross-interface 11 / 11
CVP contract 6 / 6
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 3/3 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only. Core profile does not include Live-graph integration. Label collision, near-double-root markers, viewport switching, and pointer interaction need independent visual tests.
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 sha256:0501c9b307912a2c254747057113d3b7eeb6da031feb14a87cf0a2db00b7f7d5

Input schema sha256:621584dbc2988734fc3881cb7cc96208ecf29d201fc21aee0933756e1843a5f5 · Output schema sha256:2cf2b717e03826f142557d695bfe64d52cbceaa9ce08662943e7df1504c122cc · 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: quadratic
Engine: quadratic
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-22T08:54:35.064Z
Last reviewed: —

Assumptions

a ≠ 0; coefficients are real numbers (fractions allowed).

Limitations

a = 0 → NOT_QUADRATIC
Missing coefficient → MISSING_REQUIRED_INPUT
Δ < 0 equation yields complex conjugate roots {real, imag}
Inequality is mode=inequality; discovery /quadratic-inequality
Not cubic, not CAS factoring

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, §3.4: Quadratic Equations
Supports: The quadratic formula, discriminant and real-root multiplicity. Negative discriminants have no real roots; the calculator’s complex-root representation uses the separately cited complex-number definitions. This does not validate the numerical cancellation-avoiding algorithm. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.
Gilbert Strang, Calculus — Chapter 9: Polar Coordinates and Complex Numbers (MIT OpenCourseWare) — §9.4 Complex Numbers
Supports: Complex arithmetic, conjugates, modulus and argument, polar/exponential multiplication and division, de Moivre’s formula and complex roots. Noninteger powers require a specified branch; those branch and numerical policies remain CalculatorX’s own contract. 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.