Public evidence

math.quadratic

Machine-checked verification for calculation version 1.1.0 · tier engine_tested

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

CVP: CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Core assurance· Declared partitions are two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain — 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. · Protocol · Schema · Production report

Declared partition coverage: PASS · 9/9 declared partitions (two-real, repeated, complex, irrational, near-double-root, large-scale, fraction-input, cancellation, invalid-domain)
Versions: Calculation 1.1.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 5/5 property · digest 5e416940420d

Verification

Legacy regression suite: 9/9 calculation tests · Production surface contract 4/4

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.

STALE · Last attested schema matched 1.1.0 snapshot / local build · 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 1.1.0. CVP 1.0.0-proposed. 9/9 golden · 3/3 CVP boundary · 3/3 invalid · 5/5 property · 1/1 metamorphic · 9/9 O3 · 2/2 cross-interface · 4/4 CVP contract. digest 5e416940420d. ≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, 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) 9 / 9
CVP boundary 3 / 3
Invalid input 3 / 3
Property 5 / 5
Metamorphic 1 / 1
O3 high-precision 9 / 9
Cross-interface 2 / 2
CVP contract 4 / 4
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. 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 valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS

Fingerprint sha256:296cd3ea369b5bab14dd757dc3e0665d63485936e04bee702b8a48a76a9dafeb

Input schema sha256:f5b120626630eb9452b4105cfa142b7e17dc89bcc78911c4ab09becf2080719a · Output schema sha256:ae7a578024e7d5b329eb8a7f3b30e2ba240a0b1fab47cf81938835ada4cb82a9 · 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: 2026-09-19
Evidence core: 2026-09-19T23:03:16.521Z
Rendered: 2026-09-20T09:01:32.955Z
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.

OpenStax Intermediate Algebra 2e — Quadratic Formula — 9.3 x = (−b ± √(b² − 4ac)) / (2a)
Supports: Quadratic formula and discriminant classification of the roots of ax² + bx + c = 0.
OpenStax College Algebra 2e — Quadratic Functions — 5.1 Vertex and axis of y = ax² + bx + c
Supports: Vertex / axis of symmetry of y = ax²+bx+c

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`two-real`	golden	pass	Expected x1=4 · x2=2 · delta=4 · Actual x1=4 · x2=2 · delta=4 · value=4, 2 · a=1 · b=-6 · c=8 · mode=solve
`repeated`	golden	pass	Expected x1=2 · x2=2 · delta=0 · Actual x1=2 · x2=2 · delta=0 · value=2 · a=1 · b=-4 · c=4 · mode=solve
`complex`	golden	pass	Expected delta=-16 · real=-1 · imag=2 · Actual delta=-16 · real=-1 · imag=2 · value=-1 ± 2i · a=1 · b=2 · c=5 · mode=solve
`default-two-real`	golden	pass	Expected x1=3 · x2=2 · delta=1 · Actual x1=3 · x2=2 · delta=1 · value=3, 2 · a=1 · b=-5 · c=6 · mode=solve
`irrational`	golden	pass	Expected delta=44 · Actual x1=7.3166247903554 · x2=0.6833752096446002 · delta=44 · value=7.31662479, 0.6833752096 · a=1 · b=-8 · c=5 · mode=solve
`not-quadratic`	boundary	pass	Expected NOT_QUADRATIC · Actual NOT_QUADRATIC
`cancellation`	golden	pass	Expected x2=1e-8 · Actual x1=100000000 · x2=1e-8 · delta=9999999999999996 · value=100000000, 1e-8 · a=1 · b=-100000000 · c=1 · mode=solve
`missing-a`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-quad-a0`	boundary	pass	Expected NOT_QUADRATIC · Actual NOT_QUADRATIC