{
  "capability_id": "math.numerical.derivative",
  "tool_id": "numerical-derivative",
  "engine": "numerical-derivative",
  "calculation_version": "1.1.1",
  "generated_at": "2026-10-07T06:19:46.562Z",
  "engine_build": "2026-10-07",
  "test_count": 14,
  "passed": 14,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 4,
      "total": 4
    },
    "boundary": {
      "passed": 3,
      "total": 3
    },
    "property": {
      "passed": 7,
      "total": 7
    }
  },
  "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/numerical-derivative",
  "api": "https://www.calculatorx.com/api/v1/calc/numerical-derivative",
  "schema_input": "https://www.calculatorx.com/schemas/math.numerical.derivative.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.numerical.derivative.output.json",
  "assumptions": [
    "The Result Card includes an engine-linked figure of f around x (tangent slope is the published finite difference; two-sided limit draws a horizontal at the probe). Same fnValue as REST/MCP. Not symbolic CAS d/dx.",
    "Not one-sided limits",
    "Not L’Hôpital",
    "Polynomial degree ≤ 8"
  ],
  "limitations": [
    "Not symbolic / CAS d/dx",
    "Not one-sided left/right; not L’Hôpital",
    "h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "Polynomial degree ≤ 8",
    "Not a Statistics calculator"
  ],
  "boundary_conditions": [
    "Non-finite function probes, derivative or error → NUMERICAL_RANGE_ERROR",
    "h ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "h > 1 → VALUE_OUT_OF_RANGE",
    "unknown method (including autodiff, left, lhopital, cas) → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
      "supports": "Derivative f′(x) and two-sided limit of an elementary f",
      "kind": "standard",
      "reference_scope": "all"
    },
    {
      "title": "CRC Standard Mathematical Tables — forward, backward, and central differences",
      "supports": "Forward (f(x+h)−f(x))/h; backward; central (f(x+h)−f(x−h))/(2h); two-sided probe of f",
      "kind": "reference",
      "reference_scope": "model",
      "oracle_class": "O1"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:6af89ea720b68cc1956225e58ed47961a463c14064dede0041d8032a4ee63527",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 14,
      "total": 14,
      "golden": 4,
      "boundary": 3,
      "property": 7
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-10-07T06:17:52.296Z",
  "rendered_at": "2026-10-07T06:19:46.562Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.1.1",
    "artifacts": {
      "engine": "1.1.1",
      "page": "1.1.1",
      "capability": "1.1.1",
      "evidence": "1.1.1",
      "input_schema": "1.1.1",
      "output_schema": "1.1.1",
      "mcp_contract": "1.1.1"
    },
    "digests": {
      "input_schema_sha256": "70a0ef1e57475140e9e48a5bc0b88d9aacc7d450176bf8cbe36ab7b19c8dc04e",
      "output_schema_sha256": "72d4a5122add3c5a55b71810b7173e903d9d30f93798c7d4432dac6c42c2faf9",
      "evidence_sha256": "486c32d4ec08f6660a81192c359de4f7dc71191fa17fabda412c02776b1e22a4",
      "evidence_core_sha256": "486c32d4ec08f6660a81192c359de4f7dc71191fa17fabda412c02776b1e22a4",
      "capability_sha256": "3cf8c441626c1da14d5375f2e89a64ca84c9ca87dbf951a8dd90964e6b6cad18",
      "engine_sha256": "de164a39feabc37997e09354949becc3182b03a314edbb82d01fddc018716fc0",
      "mcp_contract_sha256": "7b7034bd3fa6d4519716428728c3ed528b89f198f9444b7f1a05a92b201b5cb0"
    },
    "contract_checks": {
      "total": 4,
      "passed": 4,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.1.1"
        },
        {
          "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"
  }
}