{
  "capability_id": "electrical.rlc_resonance",
  "tool_id": "rlc-resonance",
  "engine": "rlc-resonance",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:03:43.712Z",
  "engine_build": "2026-09-10",
  "test_count": 14,
  "passed": 14,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 2,
      "passed": 2
    },
    "boundary": {
      "total": 5,
      "passed": 5
    },
    "property": {
      "total": 7,
      "passed": 7
    }
  },
  "engine_tested": true,
  "expert_reviewed": true,
  "internally_reviewed": false,
  "review_kind": "expert",
  "source_checked": true,
  "reviewed_by": "CalculatorX electrical review",
  "reviewer_role": "electrical-engineer",
  "last_reviewed": "2026-08-08",
  "expert_review": {
    "status": "approved",
    "reviewer": {
      "name": "CalculatorX electrical review",
      "role": "electrical-engineer"
    },
    "reviewed_at": "2026-08-08",
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "kind": "expert"
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/electric/rlc-resonance",
  "api": "https://www.calculatorx.com/api/v1/calc/rlc-resonance",
  "schema_input": "https://www.calculatorx.com/schemas/electrical.rlc_resonance.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/electrical.rlc_resonance.output.json",
  "assumptions": [
    "Lumped ideal R, L, C.",
    "Parallel mode is ideal R across LC (no coil ESR)."
  ],
  "limitations": [
    "Ideal lumped RLC only — not coupled coils, transmission lines, or crystal models",
    "Parallel mode assumes ideal parallel R with L and C (no ESR/ESL)",
    "Missing/non-positive L/C/R → MISSING_REQUIRED_INPUT / VALUE_MUST_BE_POSITIVE",
    "Unknown mode → INVALID_MODE"
  ],
  "boundary_conditions": [
    "Missing L/C/R → MISSING_REQUIRED_INPUT",
    "≤ 0 → VALUE_MUST_BE_POSITIVE",
    "Non-finite → INVALID_NUMBER",
    "Unknown mode → INVALID_MODE"
  ],
  "sources": [
    {
      "title": "IEC 60050 — International Electrotechnical Vocabulary",
      "section": "Resonance, quality factor, and bandwidth",
      "supports": "f₀, Q, and bandwidth definitions for resonant circuits",
      "kind": "standard"
    },
    {
      "title": "Horowitz & Hill — The Art of Electronics",
      "section": "RLC resonance, Q, and bandwidth",
      "supports": "f₀=1/(2π√(LC)); series vs parallel Q",
      "kind": "reference"
    },
    {
      "title": "NIST Guide to the SI (SP 811)",
      "section": "SI units for inductance, capacitance, and frequency",
      "url": "https://www.nist.gov/pml/special-publication-811",
      "supports": "H, F, Hz relationships",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:03a966424578294e6837b162b9ea379b5ba5afe0d01b9820f60a3d85cfcafc94",
  "tests": [
    {
      "id": "series-default",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "series",
        "L": 0.001,
        "C": 0.000001,
        "R": 10
      },
      "expect": {
        "f0": 5032.921210448703,
        "Q": 3.16227766016838,
        "BW": 1591.549430918953,
        "Z_res": 10
      },
      "expectWarning": null,
      "actual": {
        "mode": "series",
        "f0": 5032.921210448703,
        "omega0": 31622.776601683792,
        "Q": 3.16227766016838,
        "BW": 1591.549430918953,
        "X0": 31.622776601683793,
        "Z_res": 10,
        "L": 0.001,
        "C": 0.000001,
        "R": 10
      },
      "tol": 1e-9
    },
    {
      "id": "parallel-default",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "parallel",
        "L": 0.001,
        "C": 0.000001,
        "R": 10
      },
      "expect": {
        "f0": 5032.921210448703,
        "Q": 0.3162277660168379,
        "BW": 15915.494309189535
      },
      "expectWarning": null,
      "actual": {
        "mode": "parallel",
        "f0": 5032.921210448703,
        "omega0": 31622.776601683792,
        "Q": 0.3162277660168379,
        "BW": 15915.494309189535,
        "X0": 31.622776601683793,
        "Z_res": 10,
        "L": 0.001,
        "C": 0.000001,
        "R": 10
      },
      "tol": 1e-9
    },
    {
      "id": "missing-L",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "series",
        "C": 0.000001,
        "R": 10
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "L is required"
    },
    {
      "id": "zero-C",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "series",
        "L": 0.001,
        "C": 0,
        "R": 10
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "C must be greater than zero"
    },
    {
      "id": "nan-R",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "series",
        "L": 0.001,
        "C": 0.000001,
        "R": "n/a"
      },
      "expectError": "INVALID_NUMBER",
      "code": "INVALID_NUMBER",
      "error": "R must be a finite number"
    },
    {
      "id": "invalid-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dc",
        "L": 0.001,
        "C": 0.000001,
        "R": 10
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "mode must be \"series\" or \"parallel\""
    },
    {
      "id": "boundary-series-default",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "series",
        "L": 0.001,
        "C": 0.000001,
        "R": 10
      },
      "expect": {
        "f0": 5032.921210448703,
        "Q": 3.16227766016838,
        "BW": 1591.549430918953
      },
      "expectWarning": null,
      "actual": {
        "mode": "series",
        "f0": 5032.921210448703,
        "omega0": 31622.776601683792,
        "Q": 3.16227766016838,
        "BW": 1591.549430918953,
        "X0": 31.622776601683793,
        "Z_res": 10,
        "L": 0.001,
        "C": 0.000001,
        "R": 10
      },
      "tol": 1e-9
    },
    {
      "id": "property-f0",
      "ok": true,
      "kind": "property",
      "detail": "f0 from LC",
      "expect": 5032.921210448703,
      "actual": 5032.921210448703
    },
    {
      "id": "property-Qs",
      "ok": true,
      "kind": "property",
      "detail": "series Q",
      "expect": 3.16227766016838,
      "actual": 3.16227766016838
    },
    {
      "id": "property-BW",
      "ok": true,
      "kind": "property",
      "detail": "BW=f0/Q",
      "expect": 1591.549430918953,
      "actual": 1591.549430918953
    },
    {
      "id": "property-same-f0",
      "ok": true,
      "kind": "property",
      "detail": "series/parallel share f0",
      "expect": 5032.921210448703,
      "actual": 5032.921210448703
    },
    {
      "id": "property-Qp",
      "ok": true,
      "kind": "property",
      "detail": "parallel Q",
      "expect": 0.3162277660168379,
      "actual": 0.3162277660168379
    },
    {
      "id": "property-X0",
      "ok": true,
      "kind": "property",
      "detail": "X0=ω0L",
      "expect": 31.622776601683793,
      "actual": 31.622776601683793
    },
    {
      "id": "property-half-R-double-Q",
      "ok": true,
      "kind": "property",
      "detail": "½R → 2Q (series)",
      "expect": 6.32455532033676,
      "actual": 6.32455532033676
    }
  ],
  "tier": "expert_verified",
  "verification": {
    "tests": {
      "passed": 14,
      "total": 14,
      "golden": 2,
      "boundary": 5,
      "property": 7
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-05T02:35:39.217Z",
  "rendered_at": "2026-09-16T22:03:43.712Z",
  "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": "af0d832636c5bd05d0d7acab828a193972b9fe496492ccc81f7e63b90b26c5b7",
      "output_schema_sha256": "4f23bb998c98ff258e3e15be0a5aafcd9961449c77a6ef3b7f237ce5ba6bea16",
      "evidence_sha256": "7586b1b4d650b9d2463adaa11dc33d0ef07257f825e57e0cca3c77b5d0f19b05",
      "evidence_core_sha256": "7586b1b4d650b9d2463adaa11dc33d0ef07257f825e57e0cca3c77b5d0f19b05",
      "capability_sha256": "ac76fe96953c168903ddee99ba266263953f0c52cdb629d4a066c5f7d55301d0",
      "engine_sha256": "c8d4ccdbfeaf61d7b024d4e1babb0c2ba3b324c1b37bd0cb456a526d8d2b1bd1",
      "mcp_contract_sha256": "863098b311a7b17dc4b229a6302b90b3545b175f716e5d84772c7be8e9716b86"
    },
    "contract_checks": {
      "total": 4,
      "passed": 4,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}