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  "failed": 0,
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    "property": {
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  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
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    "reviewer": null,
    "scope": [
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      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
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  "assumptions": [
    "Euclidean R²/R³",
    "uz/vz/wz default to 0",
    "Not a matrix",
    "Not coordinate geometry",
    "Not CAS"
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  "limitations": [
    "R²/R³ only; uz/vz/wz default to 0",
    "Not a matrix — det / inverse / eigen stay on math.linear_algebra",
    "Not coordinate geometry (two-point line / intersection / angle between lines)",
    "Angle is the vector included angle in [0°, 180°], not the acute line angle",
    "Zero vector: magnitude 0 is valid; normalize / angle / projection → INVALID_INPUT",
    "unknown mode (including cas, eigen, matrix) → INVALID_MODE"
  ],
  "boundary_conditions": [
    "missing ux or uy → MISSING_REQUIRED_INPUT",
    "zero vector normalize / angle / projection → INVALID_INPUT",
    "unknown mode → INVALID_MODE"
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  "sources": [
    "ISO 80000-2:2019 Quantities and units — Mathematics"
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  "methods": [],
  "fingerprint": "sha256:a13c8c2eceb68442e67624cd72a734c310c0ac2e5437db2195d2c108de3b8a6c",
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      "ok": true,
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      "inputs": {
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        "ux": 3,
        "uy": 4
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      "expectWarning": null,
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        "ux": 1,
        "uy": 2,
        "uz": 3,
        "vx": 4,
        "vy": 5,
        "vz": 6
      },
      "expect": {
        "dot": 32
      },
      "expectWarning": null,
      "actual": {
        "mode": "dot",
        "ux": 1,
        "uy": 2,
        "uz": 3,
        "vx": 4,
        "vy": 5,
        "vz": 6,
        "dot": 32,
        "formula": "u · v = ux vx + uy vy + uz vz"
      },
      "tol": null
    },
    {
      "id": "golden-cross-i-j",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "cross",
        "ux": 1,
        "uy": 0,
        "uz": 0,
        "vx": 0,
        "vy": 1,
        "vz": 0
      },
      "expect": {
        "cx": 0,
        "cy": 0,
        "cz": 1
      },
      "expectWarning": null,
      "actual": {
        "mode": "cross",
        "ux": 1,
        "uy": 0,
        "uz": 0,
        "vx": 0,
        "vy": 1,
        "vz": 0,
        "cx": 0,
        "cy": 0,
        "cz": 1,
        "formula": "u × v"
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      "tol": null
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      "kind": "boundary",
      "inputs": {
        "mode": "cas",
        "ux": 1,
        "uy": 0
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be magnitude, normalize, add, sub, dot, cross, angle, projection, or triple. Not a matrix, not coordinate geometry, not CAS."
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      "inputs": {
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        "ux": 0,
        "uy": 0
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      "ok": true,
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      "detail": "i∠j=90°",
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      "id": "property-vec-triple",
      "ok": true,
      "kind": "property",
      "detail": "i·(j×k)=1",
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  "tier": "engine_tested",
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      "total": 11,
      "golden": 3,
      "boundary": 2,
      "property": 6
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