Public evidence

math.geometry.coordinate

Machine-checked verification for calculation version 1.5.0 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.5.0 · engine_tested · 21/21 tests. It is not the current published claim. Current evidence is 1.8.0 (21/21 tests) · latest.

CVP status

Not Pythagorean-only, not CAS. Discovery /line-equation, /point-line-distance, /line-intersection, /angle-between-lines. Declared partitions are the 7 published modes plus invalid-domain.

Declared partition coverage: PASS · 8/8 declared partitions (distance, midpoint, slope, line, point-line, intersect, angle, invalid-domain)
Versions: Calculation 1.5.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-22.geometry-cvp
Verification revision: 2026-09-22.geometry-cvp · 3/3 property · digest c0f46759e9a3

Verification

Legacy regression suite: 21/21 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (21/21 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 1.8.0 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 2026-09-22.geometry-cvp. Calculation version 1.5.0. CVP 1.0.0-proposed. 10/10 golden · 4/4 CVP boundary · 8/8 invalid · 3/3 property · 4/4 cross-interface · 2/2 cross-calculator · 6/6 CVP contract. digest c0f46759e9a3.

Golden (oracle-backed) 10 / 10
CVP boundary 4 / 4
Invalid input 8 / 8
Property 3 / 3
Cross-interface 4 / 4
Cross-calculator 2 / 2
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 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
schema rejects incomplete input PASS
rest success payload validates schema PASS

Fingerprint sha256:bf0bdeec4b0f52e0ff0a18c02f725e129958d490367c3acb50736782c684ac2e

Input schema sha256:af75ecf9feb03e90bfbd4fcc4e8fec32781fd18e6266fa632cb68c969f668ca2 · Output schema sha256:0a6ff13ea27d1647cd8b696249fffaa30ad5706bb2d789e0e11c1452360d1440 · 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: coordinate-geometry
Engine: coordinate-geometry
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-19T06:49:24.338Z
Last reviewed: —

Assumptions

Euclidean plane
Not 3-D / spherical

Limitations

Not the Pythagorean-only calculator — distance of (0,0) to (3,4) is the same 5 as 3-4-5, but this page is coordinates
Vertical line → slope null, vertical true
Share URLs use slope as output, not query key m
Two-point line is mode=line; coincident points → INVALID_INPUT
Point-line distance is mode=point_line; requires x0, y0; coincident line points → INVALID_INPUT
Line intersection is mode=intersect; requires x3, y3, x4, y4; parallel distinct → empty; coincident → coincident; degenerate points → INVALID_INPUT
Angle between two lines is mode=angle; requires x3, y3, x4, y4; principal angle [0°, 90°]; parallel → 0°; coincident → 0°; degenerate points → INVALID_INPUT

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 — analytic geometry
Supports: Distance √(Δx²+Δy²); point–line |Ax₀+By₀+C|/√(A²+B²); undirected line angle via atan2(|d1×d2|, |d1·d2|)
Margaret Stevens — The Maths Workbook (University of Oxford) — Chapter 2, §3: Linear Functions; Chapter 1, §4: Simultaneous Equations
Supports: Linear-function slopes and point-slope equations, and simultaneous linear equations in two variables. Line intersection is the corresponding system solution; vertical lines use an implicit rather than finite-slope representation. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.
Gilbert Strang, Calculus — Chapter 11: Vectors and Matrices (MIT OpenCourseWare) — §§11.1–11.3 Vectors, Dot Products, Projections and Cross Products
Supports: Vector components and magnitudes, dot product and angle/projection relations, and cross product/determinant orientation and area. Projecting a point displacement onto the unit normal to Ax+By+C=0 gives distance |Ax₀+By₀+C|/sqrt(A²+B²); this planar expression is derived from the projection formula. 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.