{
  "capability_id": "math.quadratic",
  "tool_id": "quadratic",
  "engine": "quadratic",
  "calculation_version": "1.1.0",
  "generated_at": "2026-10-07T03:37:48.643Z",
  "engine_build": "2026-09-19",
  "test_count": 9,
  "passed": 9,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 6,
      "total": 6
    },
    "boundary": {
      "passed": 3,
      "total": 3
    },
    "property": {
      "passed": 0,
      "total": 0
    }
  },
  "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/quadratic",
  "api": "https://www.calculatorx.com/api/v1/calc/quadratic",
  "schema_input": "https://www.calculatorx.com/schemas/math.quadratic.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.quadratic.output.json",
  "assumptions": [
    "a ≠ 0; coefficients are real numbers (fractions allowed)."
  ],
  "limitations": [
    "a = 0 → NOT_QUADRATIC",
    "Missing coefficient → MISSING_REQUIRED_INPUT",
    "Δ < 0 equation yields complex conjugate roots {real, imag}",
    "Inequality is mode=inequality; discovery /quadratic-inequality",
    "Not cubic, not CAS factoring"
  ],
  "boundary_conditions": [
    "a = 0 → rejected as not quadratic"
  ],
  "sources": [
    {
      "title": "OpenStax Intermediate Algebra 2e — Quadratic Formula",
      "section": "9.3 x = (−b ± √(b² − 4ac)) / (2a)",
      "url": "https://openstax.org/books/intermediate-algebra-2e/pages/9-3-solve-quadratic-equations-using-the-quadratic-formula",
      "supports": "Quadratic formula and discriminant classification of the roots of ax² + bx + c = 0.",
      "kind": "reference"
    },
    {
      "title": "OpenStax College Algebra 2e — Quadratic Functions",
      "section": "5.1 Vertex and axis of y = ax² + bx + c",
      "url": "https://openstax.org/books/college-algebra-2e/pages/5-1-quadratic-functions",
      "supports": "Vertex / axis of symmetry of y = ax²+bx+c",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:296cd3ea369b5bab14dd757dc3e0665d63485936e04bee702b8a48a76a9dafeb",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 9,
      "total": 9,
      "golden": 6,
      "boundary": 3,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-09-19T23:03:16.521Z",
  "rendered_at": "2026-10-07T03:37:48.643Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.1.0",
    "artifacts": {
      "engine": "1.1.0",
      "page": "1.1.0",
      "capability": "1.1.0",
      "evidence": "1.1.0",
      "input_schema": "1.1.0",
      "output_schema": "1.1.0",
      "mcp_contract": "1.1.0"
    },
    "digests": {
      "input_schema_sha256": "f5b120626630eb9452b4105cfa142b7e17dc89bcc78911c4ab09becf2080719a",
      "output_schema_sha256": "ae7a578024e7d5b329eb8a7f3b30e2ba240a0b1fab47cf81938835ada4cb82a9",
      "evidence_sha256": "1362b79bd19bfd7ac83cb8484aa45369e45a145f9bf517f2f9ce32192f669a30",
      "evidence_core_sha256": "1362b79bd19bfd7ac83cb8484aa45369e45a145f9bf517f2f9ce32192f669a30",
      "capability_sha256": "fd371e21d8d723941f8a6aad3b56c48515985e73e3d10e3837d6aaaa5c61f6e3",
      "engine_sha256": "de164a39feabc37997e09354949becc3182b03a314edbb82d01fddc018716fc0",
      "mcp_contract_sha256": "e49efe347bab0caf74bb021a2f1e2ef8154eb57be4063df0e78d3cb3146bb826"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.1.0"
        },
        {
          "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"
  }
}
