{
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  "engine_build": "2026-09-20",
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  "passed": 16,
  "failed": 0,
  "tests_summary": {
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      "passed": 5
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    "boundary": {
      "total": 3,
      "passed": 3
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    "property": {
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  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
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  "reviewer_role": null,
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      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
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    "Euclidean 3-space",
    "Right circular solids",
    "Ring torus R > r",
    "Not the circle-only page",
    "Not a vector",
    "Not ISO 5167-5",
    "Not prism / pyramid",
    "Not CAS"
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  "limitations": [
    "Right circular 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",
    "Prism / pyramid / regular solids later on this engine",
    "unknown mode (including cas, vector, iso-cone) → INVALID_MODE"
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    "r ≤ 0 or h ≤ 0 or R ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "torus R ≤ r → INVALID_INPUT",
    "frustum R ≤ 0 or r ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "unknown mode → INVALID_MODE"
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  "sources": [
    "ISO 80000-2:2019 Quantities and units — Mathematics"
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        "h": 4
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        "mode": "cone",
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        "h": 4,
        "slant": 5,
        "volume": 37.6991118431,
        "lateral": 47.1238898038,
        "surface": 75.3982236862,
        "formula": "V = (1/3)πr²h,  l = √(r²+h²)"
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    {
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        "r": 1,
        "h": 1,
        "volume": 3.14159265359,
        "lateral": 6.28318530718,
        "surface": 12.5663706144,
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    {
      "id": "boundary-solid-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "cas",
        "r": 1
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      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be sphere, cylinder, cone, torus, or frustum. Not the circle-only page, not a vector, not ISO 5167-5, not CAS."
    },
    {
      "id": "boundary-torus-horn",
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      "kind": "boundary",
      "inputs": {
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        "r": 1
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      "expectError": "INVALID_INPUT",
      "code": "INVALID_INPUT",
      "error": "Ring torus needs major radius R greater than tube radius r."
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    {
      "id": "golden-frustum-213",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "frustum",
        "R": 2,
        "r": 1,
        "h": 3
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      "expectWarning": null,
      "actual": {
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        "R": 2,
        "r": 1,
        "h": 3,
        "slant": 3.16227766017,
        "volume": 21.9911485751,
        "lateral": 29.8037647974,
        "surface": 45.5117280653,
        "cylinder": false,
        "formula": "V = (1/3)πh(R²+Rr+r²),  l = √(h²+(R−r)²)"
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      "tol": null
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    {
      "id": "golden-frustum-cyl",
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      "kind": "golden",
      "inputs": {
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        "R": 1,
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        "h": 1
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      "expectWarning": null,
      "actual": {
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        "R": 1,
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        "slant": 1,
        "volume": 3.14159265359,
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        "cylinder": true,
        "formula": "V = (1/3)πh(R²+Rr+r²),  l = √(h²+(R−r)²)"
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      "tol": null
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    {
      "id": "boundary-frustum-h",
      "ok": true,
      "kind": "boundary",
      "inputs": {
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        "R": 2,
        "r": 1,
        "h": 0
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      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "h must be positive."
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    {
      "id": "property-solid-sphere-v",
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      "kind": "property",
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