{
  "capability_id": "math.transform.laplace",
  "tool_id": "laplace-transform",
  "engine": "laplace-transform",
  "calculation_version": "1.0.0",
  "generated_at": "2026-10-09T12:41:46.230Z",
  "engine_build": "2026-09-22",
  "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/laplace-transform",
  "api": "https://www.calculatorx.com/api/v1/calc/laplace-transform",
  "schema_input": "https://www.calculatorx.com/schemas/math.transform.laplace.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.transform.laplace.output.json",
  "assumptions": [
    "Unilateral, causal t≥0",
    "Real s in the ROC",
    "Table of named pairs, not a CAS",
    "The Result Card includes an engine-linked figure of F(s) on the real ROC (pole at the ROC boundary) or f(t) for t≥0. Same table as REST/MCP.",
    "Not DFT / FFT",
    "Not Z-transform",
    "Not Bromwich / two-sided",
    "Not a pole-zero Argand of complex s"
  ],
  "limitations": [
    "Unilateral causal table only",
    "Real s in the ROC; t ≥ 0",
    "Not DFT / FFT",
    "Not Z-transform — later canonical",
    "Not Bromwich / two-sided / CAS",
    "unknown mode (including dft, z, cas) → INVALID_MODE"
  ],
  "boundary_conditions": [
    "s not in ROC → INVALID_INPUT",
    "t < 0 → INVALID_INPUT",
    "n not an integer 0–8 → INVALID_INPUT",
    "unknown mode (including dft, z, cas) → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
      "supports": "Unilateral Laplace transform of a causal elementary pair",
      "kind": "standard",
      "reference_scope": "all"
    },
    {
      "title": "Oppenheim, Willsky & Nawab, Signals and Systems — unilateral Laplace table",
      "supports": "L{e^{at}}=1/(s−a); L{1}=1/s; L{t^n}=n!/s^{n+1}; ROC Re(s)>pole",
      "kind": "reference",
      "reference_scope": "model",
      "oracle_class": "O1"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:75e50b1948e5f958df0509387b65eb3f392d9e5806bf4b358978469eabd7f50a",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 10,
      "total": 10,
      "golden": 3,
      "boundary": 2,
      "property": 5
    },
    "contract_checks": {
      "passed": 5,
      "total": 5
    }
  },
  "evidence_core_generated_at": "2026-09-22T03:44:13.208Z",
  "rendered_at": "2026-10-09T12:41:46.230Z",
  "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": "16caca56512f8a5de48c149ac283b719fba6af4ec75e4b51201d8d91109939ff",
      "output_schema_sha256": "a7515f430ae98a7c258b2896985c7756be1ce8df62a95a040b628cab896b5cf3",
      "evidence_sha256": "812d6bf045cf9a5c80a19e1b73300652869a1ba0853d4422ef3f481e18c8a127",
      "evidence_core_sha256": "812d6bf045cf9a5c80a19e1b73300652869a1ba0853d4422ef3f481e18c8a127",
      "capability_sha256": "903f70007c459d735b64a8c4a122ba9664dabfb8b8941cf0d1c5ede9e65acaca",
      "engine_sha256": "de164a39feabc37997e09354949becc3182b03a314edbb82d01fddc018716fc0",
      "mcp_contract_sha256": "b51f661a2023241687ffa11a5f1287b714fc9a5e925afa301e1c6bf2679c2d13"
    },
    "contract_checks": {
      "total": 5,
      "passed": 5,
      "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": "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"
  }
}