Public evidence

math.geometry.plane

Machine-checked verification for calculation version 1.5.0 · tier engine_tested

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Verification

25/25 calculation tests · Production surface contract 3/3

Golden tests 9 / 9
Boundary tests 5 / 5
Property tests 11 / 11
Production surface contract 3 / 3
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.5.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract PASS
Evidence attested at 2026-09-18T21:41:55.460Z
Last production check 2026-09-18T21:41:55.460Z
Public / cache —
Origin —
Supplemental domain review Not performed
Named expert review Not performed

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS

Fingerprint sha256:8b1a25bde28dba84322ff335d917d048ff26b6d93b75e2ee6c500c523b181eff

Input schema sha256:5039fac5be916efbd613bac465d29e64c0e098f17efb094b415669d76b6ace36 · Output schema sha256:4f46ff37a1617bce5f50363a965f32b87ec3740b942f35bfdb40fa31ca592515 · 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: 2026-09-20
Evidence core: 2026-09-20T13:59:38.637Z
Rendered: 2026-09-20T14:07:33.248Z
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

Euclidean plane figures only
Not the circle-only page — 2-D circle stays on math.geometry.circle
Not a triangle solver — SSS/SAS stay on math.geometry.triangle
Not solid geometry (sphere / cylinder / cone)
Regular polygon needs integer n ≥ 3
Annulus needs outer R > inner r; R = r is a circle, not an annulus
Parallelogram included angle θ must be in (0°, 180°); θ=90° recovers a rectangle
Isosceles trapezoid needs bases a,b>0 and height h>0; a=b recovers a rectangle; not the fluid trapezoid; not /trapezoidal-rule
Irregular polygon uses shoelace on 3–8 vertices; simple polygon assumed; area 0 is invalid; not /regular-polygon; not a triangle solver
unknown mode (including cas, sphere, pythagorean) → INVALID_MODE

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

Published checks

Golden, boundary, and property cases included in this evidence build.

ID	Kind	Status	Detail
`golden-rect-345`	golden	pass	Expected area=12 · perimeter=14 · diagonal=5 · Actual mode=rectangle · a=3 · b=4 · area=12 · perimeter=14 · diagonal=5 · square=false · formula=A = ab, P = 2(a+b), d = √(a²+b²)
`golden-hexagon`	golden	pass	Expected perimeter=6 · interior_deg=120 · area=2.59807621135 · Actual n=6 · mode=regular_polygon · s=1 · area=2.59807621135 · perimeter=6 · apothem=0.866025403784 · circumradius=1 · interior_deg=120
`golden-annulus`	golden	pass	Expected area=9.42477796077 · Actual mode=annulus · r=1 · R=2 · area=9.42477796077 · perimeter=18.8495559215 · outer_circumference=12.5663706144 · inner_circumference=6.28318530718 · formula=A = π(R² − r²), P = 2π(R + r)
`golden-parallelogram-30`	golden	pass	Expected area=3 · perimeter=10 · Actual mode=parallelogram · a=2 · b=3 · theta=30 · area=3 · perimeter=10 · d1=4.83655919486 · d2=1.61483595284
`golden-parallelogram-rect`	golden	pass	Expected area=12 · d1=5 · d2=5 · rectangle=true · Actual mode=parallelogram · a=3 · b=4 · theta=90 · area=12 · perimeter=14 · d1=5 · d2=5
`boundary-plane-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-polygon-n2`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-para-deg`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`golden-trapezoid-243`	golden	pass	Expected area=9 · isosceles=true · Actual mode=trapezoid · a=2 · b=4 · h=3 · height=3 · leg=3.16227766017 · midsegment=3 · area=9
`golden-trapezoid-rect`	golden	pass	Expected area=12 · perimeter=14 · rectangle=true · Actual mode=trapezoid · a=3 · b=3 · h=4 · height=4 · leg=4 · midsegment=3 · area=12
`boundary-trap-h`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`golden-irreg-16`	golden	pass	Expected n=4 · area=16 · Actual n=4 · mode=irregular_polygon · area=16 · perimeter=16.2462112512 · formula=A = (1/2)\|Σ (x_i y_{i+1} − x_{i+1} y_i)\| (shoelace)
`golden-irreg-rect`	golden	pass	Expected area=12 · perimeter=14 · Actual n=4 · mode=irregular_polygon · area=12 · perimeter=14 · formula=A = (1/2)\|Σ (x_i y_{i+1} − x_{i+1} y_i)\| (shoelace)
`boundary-irreg-n2`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`property-plane-rect-d`	property	pass	3-4 rectangle
`property-plane-hex`	property	pass	hexagon 120°
`property-plane-hex-a`	property	pass	hexagon area
`property-plane-annulus`	property	pass	annulus 2-1
`property-plane-square`	property	pass	square s=2
`property-plane-para-30`	property	pass	parallelogram 2-3-30°
`property-plane-para-rect`	property	pass	θ=90° is rectangle
`property-plane-trap-243`	property	pass	isosceles 2-4-3
`property-plane-trap-rect`	property	pass	a=b trapezoid is rectangle
`property-plane-irreg-16`	property	pass	shoelace 0,0;5,0;4,4;0,3
`property-plane-irreg-rect`	property	pass	rectangle vertices