{
  "capability_id": "math.numerical.optimize_1d",
  "tool_id": "one-dimensional-optimization",
  "engine": "one-dimensional-optimization",
  "calculation_version": "1.0.1",
  "generated_at": "2026-10-07T09:29:15.460Z",
  "engine_build": "2026-10-07",
  "test_count": 11,
  "passed": 11,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 3,
      "total": 3
    },
    "boundary": {
      "passed": 2,
      "total": 2
    },
    "property": {
      "passed": 6,
      "total": 6
    }
  },
  "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/one-dimensional-optimization",
  "api": "https://www.calculatorx.com/api/v1/calc/one-dimensional-optimization",
  "schema_input": "https://www.calculatorx.com/schemas/math.numerical.optimize_1d.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.numerical.optimize_1d.output.json",
  "assumptions": [
    "The Result Card includes an engine-linked figure of f on [a, b] (marker is published xmin, fmin; poly coeffs are read from inputs, not a REST field). Same fnValue as REST/MCP. Iterate history is not a REST field.",
    "Minimize only; f treated as unimodal on [a, b]",
    "Not multivariate and not CAS",
    "Polynomial degree ≤ 8"
  ],
  "limitations": [
    "Not multivariate / Nelder–Mead / gradient descent",
    "Not maximization (min only)",
    "a ≥ b → INVALID_INPUT",
    "Polynomial degree ≤ 8",
    "Not a CAS"
  ],
  "boundary_conditions": [
    "a ≥ b → INVALID_INPUT",
    "tol ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "unknown method (including nelder) → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
      "supports": "Minimizer of a unimodal scalar on a closed interval",
      "kind": "standard",
      "reference_scope": "all"
    },
    {
      "title": "Brent, Algorithms for Minimization without Derivatives — golden section and bounded Brent",
      "supports": "Golden-section search with φ̂=(√5−1)/2; Brent golden + inverse parabolic interpolation",
      "kind": "reference",
      "reference_scope": "model",
      "oracle_class": "O1"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:faab3d93571eda01a6e9589438c967a2594e0377a0629af9d39280f3e5d878ef",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 11,
      "total": 11,
      "golden": 3,
      "boundary": 2,
      "property": 6
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-10-07T09:27:58.515Z",
  "rendered_at": "2026-10-07T09:29:15.460Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.1",
    "artifacts": {
      "engine": "1.0.1",
      "page": "1.0.1",
      "capability": "1.0.1",
      "evidence": "1.0.1",
      "input_schema": "1.0.1",
      "output_schema": "1.0.1",
      "mcp_contract": "1.0.1"
    },
    "digests": {
      "input_schema_sha256": "a674e5d7fe0dda517a258b2be9486548ef8d3345bf2017e66c347a550682d438",
      "output_schema_sha256": "ca50b58b5c414e830a01b2ca516da96b239814f8c0a3c8eb3bb7075936986c4d",
      "evidence_sha256": "65a5e6496efbb91c0c2eea6da69e9df778c4842977f6bb042de488b5cfbfa997",
      "evidence_core_sha256": "65a5e6496efbb91c0c2eea6da69e9df778c4842977f6bb042de488b5cfbfa997",
      "capability_sha256": "a95a3429763dba38d4c8bea7a91d6bcb8cc38913368246c31a30f48c4753d397",
      "engine_sha256": "de164a39feabc37997e09354949becc3182b03a314edbb82d01fddc018716fc0",
      "mcp_contract_sha256": "0b9c789c39e56764326e61b7cd8ac48d5ecf9920c5de237ce43aaa84a48ff8b1"
    },
    "contract_checks": {
      "total": 4,
      "passed": 4,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.1"
        },
        {
          "id": "schema-output-required-declared",
          "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"
  }
}