Public evidence

math.geometry.plane

Machine-checked verification for calculation version 1.5.1 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.5.1 · engine_tested · 25/25 tests. It is not the current published claim. Current evidence is 1.6.0 (25/25 tests) · latest.

CVP status

Seven Euclidean plane shapes; strict bounded decimals, normal binary64 positive measures, exact dyadic polygon area/topology, stable ring and angle formulas; complete secondary outputs. Simple3–8 vertex polygons and safe-integer regular n; no CAS.

Declared partition coverage: PASS · 8/8 declared partitions (rectangle, square, regular-polygon, annulus, parallelogram, trapezoid, irregular-polygon, invalid-domain)
Versions: Calculation 1.5.1 · CVP protocol 1.0.0-proposed · Evidence 2026-10-28.metric-scope-v3
Verification revision: 2026-10-28.metric-scope-v3 · 4/4 property · digest 0c354d2744d9

Verification

Legacy regression suite: 25/25 calculation tests · Production surface contract 5/5

Three distinct suites: educational examples on the calculator page, this legacy regression count (25/25 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 1.6.0 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 2026-10-28.metric-scope-v3. Calculation version 1.5.1. CVP 1.0.0-proposed. 155/155 golden · 5/5 CVP boundary · 55/55 invalid · 4/4 property · 2/2 metamorphic · 5/5 cross-interface · 2/2 cross-calculator · 5/5 CVP contract. digest 0c354d2744d9.

Golden (oracle-backed) 155 / 155
CVP boundary 5 / 5
Invalid input 55 / 55
Property 4 / 4
Metamorphic 2 / 2
Cross-interface 5 / 5
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:ed5b2c0567c1f0fb08ef3bd846773138b2c121b9bad742ce7b882f213d38495d

Input schema sha256:fb5fc0f383d8c94a2115d86379345a34809706872792f5c8235afe29db9571f0 · Output schema sha256:4a40e5b192de5175b7cd2aa97fe9d357b9e7b5ce375eac4bb79637bf0b25f170 · 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: plane-geometry
Engine: plane-geometry
Engine build: 2026-10-20
Evidence core: 2026-10-20T03:50:04.347Z
Rendered: 2026-10-29T07:58:56.690Z
Last reviewed: —

Assumptions

Euclidean plane
Regular polygon integer n ≥ 3
Annulus R > r
Parallelogram θ in (0°, 180°)
Isosceles trapezoid a, b, h > 0
Irregular polygon shoelace 3–8 vertices
Not the circle-only page
Not a triangle solver
Not solid geometry
Not /trapezoidal-rule
Not the fluid trapezoid
Not CAS

Limitations

Positive dimensions and nonzero coordinates must be finite normal binary64; exact zero coordinates allowed. Positive reported measures must be normal binary64. Strict bounded decimal texts and matching active aliases.
Regular n is an integer3–9007199254740991; figures draw at most128 sides, otherwise explicitly omitted.
Simple polygon3–8 ordered distinct vertices, optional closing repetition. Exact predicates reject crossings, nonadjacent contacts, overlaps, backtracking and zero area. Concave, clockwise and collinear nonoverlapping intermediate vertices supported.
Annulus R>r>0; parallelogram0<theta<180 degrees with normal radian conversion; trapezoid assumes isosceles legs.
Thin rings/near-flat figures/topology are sensitive to input rounding. Exact predicates concern normalized binary64, not original arbitrary-precision decimals. Verification relative1e-11 is arithmetic, not input perturbation accuracy.
NUMERIC_UNDERFLOW for nonzero text converted to zero; NUMERIC_RANGE for nonnormal inputs/outputs. Change length units or translate coordinates. No absolute zero clamp.
Interactive solve local; shared URLs, REST/MCP and analytics have separate disclosed data paths.

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 — plane polygons
Supports: Regular n-gon A = (n s²)/(4 tan(π/n)); parallelogram A = ab sin θ; shoelace / Meister–Gauss polygon area
Euclid’s Elements — I.35: Parallelograms on the Same Base
Supports: Equal-base, equal-height parallelograms have equal area. Comparing with a rectangle gives A = base × perpendicular height; side length is not generally the height. Mathematical reference only; not validation or endorsement of this implementation.
Gilbert Strang, Calculus — Chapter 9: Polar Coordinates and Complex Numbers (MIT OpenCourseWare) — §§9.1–9.3 Polar Coordinates, Length and Area
Supports: Polar coordinates and the circular wedge area r²Δθ/2, together with area = ∫r² dθ/2 and polar arc-length integration. A full turn gives disk area πr² and circumference 2πr. An annulus follows by subtracting disk areas and adding both boundary lengths; these are derived applications. 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.
Gilbert Strang, Calculus — Chapter 1: Introduction to Calculus (MIT OpenCourseWare) — §1.5 A Review of Trigonometry
Supports: Right-triangle definitions of sine, cosine and tangent, the sine/cosine identities, and the law-of-cosines and parallelogram exercises 31–32. Chord length follows by bisecting the radii triangle. Regular-polygon apothems and areas follow by splitting the polygon into equal triangles. The law of sines follows by equating a triangle’s altitude computed from either adjacent side; SSA can give two triangles. These applications are derived from the stated relations. 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.