{
  "capability_id": "math.numerical.ode",
  "tool_id": "ordinary-differential-equation",
  "engine": "ordinary-differential-equation",
  "calculation_version": "1.0.2",
  "generated_at": "2026-10-07T12:07:53.365Z",
  "engine_build": "2026-10-07",
  "test_count": 9,
  "passed": 9,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 3,
      "total": 3
    },
    "boundary": {
      "passed": 2,
      "total": 2
    },
    "property": {
      "passed": 4,
      "total": 4
    }
  },
  "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/ordinary-differential-equation",
  "api": "https://www.calculatorx.com/api/v1/calc/ordinary-differential-equation",
  "schema_input": "https://www.calculatorx.com/schemas/math.numerical.ode.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.numerical.ode.output.json",
  "assumptions": [
    "The Result Card includes an engine-linked Live graph of numerical y(t) using the same Overview / Focus template as Log (Overview window t0…t1; current point is published y(t1); same Euler/RK4 stepper as REST/MCP). Exact y(t1) is a reference when it differs. Not rk45, not systems, not PDE, not CAS.",
    "Scalar first-order only",
    "Polynomial degree ≤ 8"
  ],
  "limitations": [
    "Not rk45 / adaptive / Dormand–Prince",
    "Not systems of ODEs or second-order IVP",
    "Not PDE / CAS / symbolic solve",
    "n ≤ 10000",
    "t1 = t0 → INVALID_INPUT"
  ],
  "boundary_conditions": [
    "Unrepresentable time grid, zero/nonfinite h, nonfinite step/reference/error → NUMERICAL_RANGE_ERROR",
    "t1 = t0 → INVALID_INPUT",
    "n < 1 or n > 10000 → INVALID_INPUT",
    "unknown method (including rk45) → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
      "supports": "Scalar first-order IVP y′=f(t,y), y(t0)=y0",
      "kind": "standard",
      "reference_scope": "all"
    },
    {
      "title": "CRC Standard Mathematical Tables — Euler and classical RK4",
      "supports": "Forward Euler y ← y+h f; classical RK4 four-stage step; exact y0 e^{kΔt} for y′=ky",
      "kind": "reference",
      "reference_scope": "model",
      "oracle_class": "O1"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:fe76f3ce2e0a4f8d6432922d48afffe78408eeabc0b5cae1d2a26cf1c1fa6eeb",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 9,
      "total": 9,
      "golden": 3,
      "boundary": 2,
      "property": 4
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-10-07T12:05:50.870Z",
  "rendered_at": "2026-10-07T12:07:53.365Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.2",
    "artifacts": {
      "engine": "1.0.2",
      "page": "1.0.2",
      "capability": "1.0.2",
      "evidence": "1.0.2",
      "input_schema": "1.0.2",
      "output_schema": "1.0.2",
      "mcp_contract": "1.0.2"
    },
    "digests": {
      "input_schema_sha256": "f53ee0d062e34352be454eb0d34f4472ab009ce392af895e7fe579120386e4ac",
      "output_schema_sha256": "bb4f82942f9af59b2b122db518f6ca72b7ec00beb210164c6d02bd1be367f6b6",
      "evidence_sha256": "19183313166e07d24630fb8a72fdd63afe3082bfcff05f305ce693d36c8170bf",
      "evidence_core_sha256": "19183313166e07d24630fb8a72fdd63afe3082bfcff05f305ce693d36c8170bf",
      "capability_sha256": "41cc3fb1f200fbdbadb45a3620abce21df4dd1f608b1307fab124582e8162e04",
      "engine_sha256": "de164a39feabc37997e09354949becc3182b03a314edbb82d01fddc018716fc0",
      "mcp_contract_sha256": "5ab923d8ce85be31f4b9e5ba2a1ff2c2298c3df9f6cba201fbdc930300d128b1"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.2"
        },
        {
          "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"
  }
}