Public evidence

math.geometry.circle

Machine-checked verification for calculation version 1.1.1 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.1.1 · engine_tested · 10/10 tests. It is not the current published claim. Current evidence is 1.2.0 (10/10 tests) · latest.

CVP status

Plane Euclidean circle only. Discovery /sector, /arc lock one mode. Not Pythagorean, not /spherical-sector, not CAS. Declared partitions are the 6 published modes plus invalid-domain.

Declared partition coverage: PASS · 7/7 declared partitions (from-radius, from-diameter, from-circumference, from-area, arc, sector, invalid-domain)
Versions: Calculation 1.1.1 · CVP protocol 1.0.0-proposed · Evidence 2026-10-14.circle-mode-provenance-v4
Verification revision: 2026-10-14.circle-mode-provenance-v4 · 4/4 property · digest 4c747b0b874a

Verification

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

Three distinct suites: educational examples on the calculator page, this legacy regression count (10/10 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.

STALE · Build schema 1.2.0 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 2026-10-14.circle-mode-provenance-v4. Calculation version 1.1.1. CVP 1.0.0-proposed. 10/10 golden · 6/6 CVP boundary · 14/14 invalid · 4/4 property · 4/4 cross-interface · 3/3 cross-calculator · 5/5 CVP contract. digest 4c747b0b874a.

Golden (oracle-backed) 10 / 10
CVP boundary 6 / 6
Invalid input 14 / 14
Property 4 / 4
Cross-interface 4 / 4
Cross-calculator 3 / 3
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:cf0fb197ed66512afbac61b96e16356d3fc46620a29204e833e53dfbdd893098

Input schema sha256:9e5a28fc177e3a7c4180b79555a0d41716ffa33772d022add93cd61d40106165 · Output schema sha256:3268110420103ee9b8de4abd7b29f616ee63685891bd40e51ca1120334d8f2c4 · 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: circle
Engine: circle
Engine build: 2026-10-14
Evidence core: 2026-10-14T09:14:32.835Z
Rendered: 2026-10-15T07:25:26.665Z
Last reviewed: —

Assumptions

Euclidean plane
Not spherical geometry
Not Pythagorean-only

Limitations

Not a²+b²=c² — use /calc/math/pythagorean
r ≤ 0 → VALUE_MUST_BE_POSITIVE
Spherical geometry is out of scope
All nonzero outputs must be finite normal binary64 values (magnitude at least 2^-1022); exact zero angles are supported. Outside this envelope, NUMERIC_RANGE requests rescaling instead of returning zero, Infinity, or NaN.

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 circle
Supports: C = 2πr, A = πr², arc s = rθ, sector A = (1/2)r²θ with θ in radians
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 1: Introduction to Calculus (MIT OpenCourseWare) — §§1.4–1.5 Circular Motion and A Review of Trigonometry
Supports: Radians, the equivalence of 360° and 2π radians, and circular circumference 2πr. Scaling the unit-circle distance gives arc length s = rθ; right-triangle sine gives chord length 2r sin(θ/2). Signed angles and multi-turn behavior are CalculatorX’s explicit policy. 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.