Public evidence

math.geometry.conic

Machine-checked verification for calculation version 1.1.0 · tier candidate

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

All three axis-aligned modes; both orientations/signs; normalized binary64 inputs, finite normal nonzero outputs. Ramanujan I perimeter is approximate. Near-circle conditioning and saturated eccentricity are documented. Independent mpmath750 fixtures; no rotated/translated conics.

Declared partition coverage: PASS · 4/4 declared partitions (ellipse, parabola, hyperbola, invalid-domain)
Versions: Calculation 1.1.0 · CVP protocol 1.0.0-proposed · Evidence 2026-10-29.math-uuce-fields-v1
Verification revision: 2026-10-29.math-uuce-fields-v1 · 3/3 property · digest e1dc06efeffb

Verification

Legacy regression suite: 9/10 calculation tests · Production surface contract 5/5 · 1 failed

Three distinct suites: educational examples on the calculator page, this legacy regression count (9/10 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 1.1.0 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 2026-10-29.math-uuce-fields-v1. Calculation version 1.1.0. CVP 1.0.0-proposed. 185/185 golden · 2/2 CVP boundary · 49/49 invalid · 3/3 property · 4/4 metamorphic · 4/4 cross-interface · 2/2 cross-calculator · 5/5 CVP contract. digest e1dc06efeffb.

Golden (oracle-backed) 185 / 185
CVP boundary 2 / 2
Invalid input 49 / 49
Property 3 / 3
Metamorphic 4 / 4
Cross-interface 4 / 4
Cross-calculator 2 / 2
CVP contract 5 / 5
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (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.
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
rest success payload validates schema PASS

Fingerprint sha256:0db2dbae6a1b14b23c2a7ab6c7be3fae79d804efa8a2aa97145fb21b19a96b45

Input schema sha256:b88e095517f0e4e990ba0670d326cf0c4d11bc64c5f7e91fa5599d75bb6d296b · Output schema sha256:ad16228467fc0090fb62374d9284f144784837b826dc4737ac334713e6e14ec4 · 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: conic-section
Engine: conic-section
Engine build: 2026-10-29
Evidence core: 2026-10-29T08:55:15.563Z
Rendered: 2026-11-10T05:18:42.114Z
Last reviewed: —

Assumptions

Euclidean plane
Axis-aligned standard forms
Not rotated (no xy term)
Not translated
Not the circle-only page
Not coordinate geometry
Not CAS

Limitations

Axis-aligned standard forms only; not rotated (xy term), not translated
Not the circle-only calculator — a=b is a valid ellipse with e=0; /calc/math/circle stays the circle page
Not coordinate geometry (two-point line / intersection / angle)
Ellipse perimeter is Ramanujan I, not a complete elliptic integral
a ≤ 0 or b ≤ 0 → VALUE_MUST_BE_POSITIVE
parabola p = 0 → INVALID_INPUT
unknown mode (including cas, circle, pythagorean) → INVALID_MODE
Decimal inputs normalize to binary64; circle uses exact a===b after normalization. Near-circle c/e are sensitive to input rounding; noncircle eccentricity may round to1.
Nonzero input/output scalars must be finite normal binary64; NUMERIC_RANGE requires rescaling. No absolute-zero clamp. Explicit empty/null inputs reject; inactive supplied numeric fields are validated.
Ellipse perimeter is Ramanujan I approximation, not exact arclength. Relative2e-12 verification compares the stated approximation formula, not its model error.
Local browser calculation; shared URLs are received by the server; REST/MCP send their inputs.

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.
S. Ramanujan — Modular Equations and Approximations to π (1914)
Supports: Ellipse perimeter approximation I: π[3(a+b)−√((3a+b)(a+3b))]; not an elliptic integral
NIST DLMF — 19.30 Lengths of Plane Curves — 19.30(i), especially equation 19.30.5
Supports: Exact ellipse perimeter L(a,b) = 4a E(k), with k² = 1−b²/a² and a ≥ b. A displayed elementary perimeter approximation is distinct from this exact elliptic-integral definition; the reference does not establish the approximation’s error or validate CalculatorX.
Gilbert Strang, Calculus — Chapter 3: Applications of the Derivative (MIT OpenCourseWare) — §3.5 Parabolas, Ellipses, and Hyperbolas
Supports: Standard equations and focal geometry of axis-aligned conic sections, including translated equations and the ellipse’s semiaxes. Ellipse area and perimeter are supported by separate integral references. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.
Gilbert Strang, Calculus — Chapter 15: Vector Calculus (MIT OpenCourseWare) — §15.3 Green’s Theorem
Supports: The planar area formula A = (1/2) ∮(x dy − y dx). For straight polygon edges it gives the shoelace expression; rectangular/square areas and trapezoid area (B+b)h/2 follow by applying it to the vertices. For x=a cos t, y=b sin t it gives ellipse area πab. Perimeters of these polygons are sums of side lengths. These formulas are derived applications of the theorem. 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.