{
  "capability_id": "math.geometry.triangle",
  "tool_id": "triangle-solver",
  "engine": "triangle-solver",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:38:08.874Z",
  "engine_build": "2026-09-16",
  "test_count": 10,
  "passed": 10,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 3,
      "passed": 3
    },
    "boundary": {
      "total": 2,
      "passed": 2
    },
    "property": {
      "total": 5,
      "passed": 5
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/math/triangle-solver",
  "api": "https://www.calculatorx.com/api/v1/calc/triangle-solver",
  "schema_input": "https://www.calculatorx.com/schemas/math.geometry.triangle.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.geometry.triangle.output.json",
  "assumptions": [
    "Euclidean plane",
    "Not spherical trigonometry",
    "Not Pythagorean-only"
  ],
  "limitations": [
    "Not the right-triangle Pythagorean calculator — use /calc/math/pythagorean",
    "SSS failing triangle inequality → INVALID_INPUT",
    "SSA may return status multiple_solutions",
    "Spherical / spherical excess is out of scope"
  ],
  "boundary_conditions": [
    "triangle inequality fail → INVALID_INPUT",
    "unknown mode (including hl) → INVALID_MODE"
  ],
  "sources": [
    "ISO 80000-2:2019 Quantities and units — Mathematics"
  ],
  "methods": [],
  "fingerprint": "sha256:79ea6b9a97338fab22da300210933943c10643325e686292cb63fd5d0e85e229",
  "tests": [
    {
      "id": "golden-345",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "sss",
        "a": 3,
        "b": 4,
        "c": 5
      },
      "expect": {
        "C_deg": 90,
        "area": 6
      },
      "expectWarning": null,
      "actual": {
        "mode": "sss",
        "status": "success",
        "solution_count": 1,
        "solutions": [
          {
            "a": 3,
            "b": 4,
            "c": 5,
            "A_deg": 36.8698976458,
            "B_deg": 53.1301023542,
            "C_deg": 90,
            "area": 6,
            "perimeter": 12
          }
        ],
        "a": 3,
        "b": 4,
        "c": 5,
        "A_deg": 36.8698976458,
        "B_deg": 53.1301023542,
        "C_deg": 90,
        "area": 6,
        "perimeter": 12,
        "formula": "law of sines / law of cosines",
        "model": "euclidean_triangle"
      },
      "tol": 1e-8
    },
    {
      "id": "golden-equilateral-sas",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "sas",
        "a": 5,
        "b": 5,
        "C_deg": 60
      },
      "expect": {
        "A_deg": 60,
        "B_deg": 60,
        "C_deg": 60
      },
      "expectWarning": null,
      "actual": {
        "mode": "sas",
        "status": "success",
        "solution_count": 1,
        "solutions": [
          {
            "a": 5,
            "b": 5,
            "c": 5,
            "A_deg": 60,
            "B_deg": 60,
            "C_deg": 60,
            "area": 10.8253175473,
            "perimeter": 15
          }
        ],
        "a": 5,
        "b": 5,
        "c": 5,
        "A_deg": 60,
        "B_deg": 60,
        "C_deg": 60,
        "area": 10.8253175473,
        "perimeter": 15,
        "formula": "law of sines / law of cosines",
        "model": "euclidean_triangle"
      },
      "tol": 0.000001
    },
    {
      "id": "golden-ssa-ambiguous",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "ssa",
        "a": 7,
        "A_deg": 30,
        "b": 10
      },
      "expect": {
        "status": "multiple_solutions",
        "solution_count": 2
      },
      "expectWarning": null,
      "actual": {
        "mode": "ssa",
        "status": "multiple_solutions",
        "solution_count": 2,
        "solutions": [
          {
            "a": 7,
            "b": 10,
            "c": 13.5592335234,
            "A_deg": 30,
            "B_deg": 45.5846914028,
            "C_deg": 104.415308597,
            "area": 33.8980838085,
            "perimeter": 30.5592335234
          },
          {
            "a": 7,
            "b": 10,
            "c": 3.76127455228,
            "A_deg": 30,
            "B_deg": 134.415308597,
            "C_deg": 15.5846914028,
            "area": 9.4031863807,
            "perimeter": 20.7612745523
          }
        ],
        "a": 7,
        "b": 10,
        "c": 13.5592335234,
        "A_deg": 30,
        "B_deg": 45.5846914028,
        "C_deg": 104.415308597,
        "area": 33.8980838085,
        "perimeter": 30.5592335234,
        "formula": "law of sines (SSA)",
        "model": "euclidean_triangle"
      },
      "tol": null
    },
    {
      "id": "boundary-triangle-inequality",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "sss",
        "a": 1,
        "b": 1,
        "c": 3
      },
      "expectError": "INVALID_INPUT",
      "code": "INVALID_INPUT",
      "error": "Sides do not satisfy the triangle inequality."
    },
    {
      "id": "boundary-triangle-pythag",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "hl",
        "a": 3,
        "b": 4,
        "c": 5
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be sss, sas, asa, aas, or ssa."
    },
    {
      "id": "property-tri-right",
      "ok": true,
      "kind": "property",
      "detail": "3-4-5 right",
      "expect": 90,
      "actual": 90
    },
    {
      "id": "property-tri-area",
      "ok": true,
      "kind": "property",
      "detail": "area 6",
      "expect": 6,
      "actual": 6
    },
    {
      "id": "property-tri-sum",
      "ok": true,
      "kind": "property",
      "detail": "angle sum",
      "expect": 180,
      "actual": 180
    },
    {
      "id": "property-tri-equil",
      "ok": true,
      "kind": "property",
      "detail": "SAS 60° isosceles",
      "expect": 5,
      "actual": 5
    },
    {
      "id": "property-tri-ssa",
      "ok": true,
      "kind": "property",
      "detail": "SSA ambiguous",
      "expect": 2,
      "actual": 2
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 10,
      "total": 10,
      "golden": 3,
      "boundary": 2,
      "property": 5
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-16T14:46:01.365Z",
  "rendered_at": "2026-09-16T22:38:08.874Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
      "engine": "1.0.0",
      "page": "1.0.0",
      "capability": "1.0.0",
      "evidence": "1.0.0",
      "input_schema": "1.0.0",
      "output_schema": "1.0.0",
      "mcp_contract": "1.0.0"
    },
    "digests": {
      "input_schema_sha256": "500518296c4124ee1ba2d295773ad62b6fa78427e229a5d95e2f6d08efb5c69d",
      "output_schema_sha256": "b0ab7fd6fa4e01dee6e9346d8f5c424bff0e9b253a5b1edf9e13841ceaed901f",
      "evidence_sha256": "9451991abe70ea84dc7255167e2a13c15acaec7af3d6fcf69b398f08a7b4c982",
      "evidence_core_sha256": "9451991abe70ea84dc7255167e2a13c15acaec7af3d6fcf69b398f08a7b4c982",
      "capability_sha256": "4753c7c67deca730e20433144f92de15fb7491ff884f40d9643cfc9d23f9f434",
      "engine_sha256": "c8d4ccdbfeaf61d7b024d4e1babb0c2ba3b324c1b37bd0cb456a526d8d2b1bd1",
      "mcp_contract_sha256": "863098b311a7b17dc4b229a6302b90b3545b175f716e5d84772c7be8e9716b86"
    },
    "contract_checks": {
      "total": 4,
      "passed": 4,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}
