math.geometry.solid

• Golden tests 42 / 42
• Boundary tests 23 / 23
• Property tests 46 / 46
• Production surface contract 3 / 3
}
• Engine tested Yes
• Source checked Yes
• Artifact integrity PASS
• Production attestation Embedded snapshot: unpublished · Build schema 1.18.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain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 sha256:0cd74db867842c953153bb45e8972a64f303cdc04aec1eeb835bbaad82cf09b3

Input schema sha256:326ca21e48f914191896910b3741753c3a4eb47743b0edbe256ec6782ba4b0ce · Output schema sha256:ccf3ddbe08d3862b21c575bcb7f654289a480faf5245cf25e58b8c4d1a9d6f79 · 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.

Tool

solid-geometry

Engine

solid-geometry

Engine build

2026-09-20

Evidence core

2026-09-20T13:37:57.245Z

Rendered

2026-09-20T14:07:33.247Z

Last reviewed

—

Assumptions

• Euclidean 3-space
• Right solids; not oblique
• Ring torus R > r
• Not the circle-only page
• Not a vector
• Not ISO 5167-5
• Not a sphere page for ellipsoid
• Not CAS

Limitations

• Right solids only; not oblique
• Not the circle-only page — 2-D circle stays on math.geometry.circle
• Not a vector — math.vector is R²/R³ algebra
• Not ISO 5167-5 cone meter (physics.fluid.iso_cone)
• Torus is a ring torus: major R > tube r; horn/spindle out of scope
• Right circular frustum needs R,r,h>0; r=R recovers a cylinder; not a cone page
• Right rectangular prism needs a,b,h>0; a=b=h is a cube; not a frustum page
• Right rectangular pyramid needs a,b,h>0; V=abh/3; apex above the base center; a=b is a square base; not a prism page
• Regular tetrahedron needs a>0; V=a³√2/12, A=a²√3; not a rectangular pyramid page
• Regular octahedron needs a>0; V=(√2/3)a³, A=2√3 a²; not a tetrahedron page
• Regular icosahedron needs a>0; V=(5/12)(3+√5)a³, A=5√3 a²; not an octahedron page
• Regular dodecahedron needs a>0; V=(1/4)(15+7√5)a³, A=3√(25+10√5) a²; not an icosahedron page
• Regular n-gon prism needs integer n≥3 and s,h>0; base from math.geometry.plane; n=4 matches a square rectangular prism; not /prism; not an n-gon pyramid
• Regular n-gon pyramid needs integer n≥3 and s,h>0; V=A h/3 with A from math.geometry.plane; n=4 matches a square rectangular pyramid; not /pyramid; not a tetrahedron; not /regular-frustum
• Regular n-gon frustum needs integer n≥3 and s,t,h>0; V=h/3(A+a+√(Aa)) with A,a from math.geometry.plane; s=t recovers a regular prism; lateral faces from the plane isosceles trapezoid; not /frustum; not /regular-pyramid
• Ellipsoid needs a,b,c>0; V=4/3 πabc; surface from spheroid closed forms or incomplete elliptic F,E; a=b=c is a sphere; not /sphere; not the 2-D ellipse
• Spherical cap needs r>0 and 0<h≤2r; V=(1/3)πh²(3r−h); h=r is a hemisphere; h=2r is a sphere; not /sphere; not a spherical zone
• Spherical zone needs a,b,h>0; V=(πh/6)(3a²+3b²+h²); r recovered; a=b is symmetric; not /spherical-cap; not /sphere; not a spherical wedge
• Spherical wedge needs r>0 and 0<θ≤360°; V=(2/3)r³θ with θ in radians; θ=180° is a hemisphere; θ=360° is a sphere; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical lune
• Spherical lune needs r>0 and 0<θ≤360°; A=2r²θ with θ in radians; θ=180° is a hemisphere surface; θ=360° is a sphere; not /spherical-wedge; not /spherical-cap; not /spherical-zone; not /sphere; not a spherical sector
• Spherical sector needs r>0 and 0<h≤2r; V=(2/3)πr²h; a=√(h(2r−h)); A=πr(2h+a); h=r is a hemisphere; h=2r is a sphere; not /spherical-cap; not /cone; not /sphere; not /spherical-wedge; not /spherical-lune
• unknown mode (including cas, vector, iso-cone) → INVALID_MODE