{
  "capability_id": "math.geometry.triangle",
  "tool_id": "triangle-solver",
  "engine": "triangle-solver",
  "calculation_version": "1.0.0",
  "generated_at": "2026-10-20T01:56:50.906Z",
  "engine_build": "2026-10-14",
  "test_count": 10,
  "passed": 10,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 3,
      "total": 3
    },
    "boundary": {
      "passed": 2,
      "total": 2
    },
    "property": {
      "passed": 5,
      "total": 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": [
    {
      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
      "url": "https://www.iso.org/standard/64973.html",
      "supports": "Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.",
      "kind": "standard",
      "publisher": "International Organization for Standardization",
      "reference_scope": "all"
    },
    {
      "title": "CRC Standard Mathematical Tables — law of sines and cosines",
      "supports": "SSS/SAS/ASA/AAS law of cosines; SSA law of sines including the ambiguous case",
      "kind": "reference",
      "reference_scope": "model",
      "oracle_class": "O1"
    },
    {
      "title": "Gilbert Strang, Calculus — Chapter 1: Introduction to Calculus (MIT OpenCourseWare)",
      "section": "§1.5 A Review of Trigonometry",
      "url": "https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch01.pdf",
      "supports": "Right-triangle definitions of sine, cosine and tangent, the sine/cosine identities, and the law-of-cosines and parallelogram exercises 31–32. Chord length follows by bisecting the radii triangle. Regular-polygon apothems and areas follow by splitting the polygon into equal triangles. The law of sines follows by equating a triangle’s altitude computed from either adjacent side; SSA can give two triangles. These applications are derived from the stated relations. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.",
      "kind": "reference",
      "publisher": "Wellesley-Cambridge Press; hosted by MIT OpenCourseWare"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:79ea6b9a97338fab22da300210933943c10643325e686292cb63fd5d0e85e229",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 10,
      "total": 10,
      "golden": 3,
      "boundary": 2,
      "property": 5
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-10-14T05:05:51.930Z",
  "rendered_at": "2026-10-20T01:56:50.906Z",
  "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": "c56de12295ecd3b760d0aee372e1b993ec5f3184eea186e87e6166614c5d3dfd",
      "evidence_core_sha256": "c56de12295ecd3b760d0aee372e1b993ec5f3184eea186e87e6166614c5d3dfd",
      "capability_sha256": "81ec05d323b19698416e1904197a01ced55201258f0254d62ba61f5d5f67ee5d",
      "engine_sha256": "6ef38e64f6a7018cce0538e78ba57c8e2a141f11e8779e9e3f91408a668b7b71",
      "mcp_contract_sha256": "e0a443d77b220f742e794adf783094e9c029072612faab445ebb52ad0a49c229"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  },
  "tests": [],
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}
