{
  "capability_id": "electrical.rf.smith",
  "tool_id": "smith-chart",
  "engine": "smith-chart",
  "calculation_version": "1.6.3",
  "generated_at": "2026-09-16T22:03:43.750Z",
  "engine_build": "2026-09-10",
  "test_count": 21,
  "passed": 21,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 9,
      "passed": 9
    },
    "boundary": {
      "total": 5,
      "passed": 5
    },
    "property": {
      "total": 7,
      "passed": 7
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": true,
  "review_kind": "internal",
  "source_checked": true,
  "reviewed_by": "CalculatorX Internal RF review",
  "reviewer_role": "Internal RF review",
  "last_reviewed": "2026-08-09",
  "expert_review": {
    "status": "not_applicable",
    "reviewer": null,
    "note": "Internal domain review completed; not a named external expert review.",
    "kind": "internal"
  },
  "internal_review": {
    "status": "approved",
    "reviewer": {
      "name": "CalculatorX Internal RF review",
      "role": "Internal RF review"
    },
    "reviewed_at": "2026-08-09",
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "kind": "internal"
  },
  "page": "https://www.calculatorx.com/calc/electric/smith-chart",
  "api": "https://www.calculatorx.com/api/v1/calc/smith-chart",
  "schema_input": "https://www.calculatorx.com/schemas/electrical.rf.smith.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/electrical.rf.smith.output.json",
  "assumptions": [
    "Impedance / matching workspace: passive loads with R≥0 (short and pure reactance allowed on |Γ|=1)",
    "Chart / Z↔Γ / matching steps operate in passive region |Γ|≤1; active-device overlays (stability/gain/noise) are analysis aids and may reference circles that extend outside the unit circle but load markers remain clipped to |Γ|≤1",
    "Looking toward generator; lossless line/stub unless R/‖RLC added; narrowband"
  ],
  "limitations": [
    "No multi-section Chebyshev / broadband optimizer",
    "Full bilateral gain redesign with S12 feedback not supported",
    "Drag-to-tune and S21/stability overlays are UI-side (API returns numerical modes)",
    "Noise circles require Touchstone noise params (NFmin, Γopt, Rn); not inferred from S alone",
    "Passive Z↔Γ / matching: R≥0 and |Γ|≤1; active overlay circles may extend outside the unit circle"
  ],
  "boundary_conditions": [
    "R<0 or r<0 → NEGATIVE_RESISTANCE_NOT_SUPPORTED (R=0 short / pure jX allowed)",
    "|Γ|>1 → VALUE_OUT_OF_RANGE for Z↔Γ / matching (passive mode); active overlay circles may extend outside unit circle",
    "L/C/R ≤0 → VALUE_MUST_BE_POSITIVE",
    "stub near open/short poles → VALUE_OUT_OF_RANGE",
    "Noise circles require Touchstone noise params (NFmin, Γopt, Rn); not inferred from S alone"
  ],
  "sources": [
    {
      "title": "Pozar Microwave Engineering",
      "section": "Smith chart / matching",
      "supports": "Γ↔z, L-section, single-stub, λ/4, stability circles",
      "kind": "reference"
    },
    {
      "title": "Keysight — Data Format and Scale (Smith / polar)",
      "section": "Smith chart maps Γ to normalized impedance; constant-r / constant-x",
      "supports": "Professional Smith display semantics (R+jX, Γ, SWR)",
      "kind": "reference"
    },
    {
      "title": "IBIS Open Forum — Touchstone File Format Specification 2.1",
      "section": "Reference specification (Touchstone 2.1); CalculatorX implements a Touchstone 1.x compatible subset",
      "supports": "Option-line semantics, S-parameter formats, reference impedance (parser: 1.x subset)",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:7ace186bc38978d6caea5c8694605a6e778f40e10ebfd9d79331688a07e99ef5",
  "tests": [
    {
      "id": "z-gamma",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "z-gamma",
        "z_r": 2,
        "z_i": 0
      },
      "expect": {
        "gamma_r": 0.3333333333333333,
        "VSWR": 2
      },
      "expectWarning": null,
      "actual": {
        "mode": "z-gamma",
        "z_r": 2,
        "z_i": 0,
        "y_r": 0.5,
        "y_i": 0,
        "gamma_r": 0.3333333333333333,
        "gamma_i": 0,
        "gamma_mag": 0.3333333333333333,
        "gamma_angle_deg": 0,
        "VSWR": 1.9999999999999998,
        "RL_dB": 9.54242509439325,
        "chart_x": 337.3333333333333,
        "chart_y": 260
      },
      "tol": 1e-12
    },
    {
      "id": "short",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "z-gamma",
        "z_r": 0,
        "z_i": 0
      },
      "expect": {
        "gamma_r": -1,
        "gamma_i": 0,
        "gamma_mag": 1
      },
      "expectWarning": null,
      "actual": {
        "mode": "z-gamma",
        "z_r": 0,
        "z_i": 0,
        "y_r": null,
        "y_i": 0,
        "gamma_r": -1,
        "gamma_i": 0,
        "gamma_mag": 1,
        "gamma_angle_deg": 180,
        "VSWR": null,
        "RL_dB": 0,
        "chart_x": 28,
        "chart_y": 260
      },
      "tol": 1e-12
    },
    {
      "id": "bad",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "z-gamma",
        "z_r": -0.1,
        "z_i": 0
      },
      "expectError": "NEGATIVE_RESISTANCE_NOT_SUPPORTED",
      "code": "NEGATIVE_RESISTANCE_NOT_SUPPORTED",
      "error": "z_r (normalized resistance) must be ≥ 0"
    },
    {
      "id": "ts-empty",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "s11-touchstone",
        "touchstone": ""
      },
      "expectError": "TOUCHSTONE_MISSING_PARAMETER",
      "code": "TOUCHSTONE_MISSING_PARAMETER",
      "error": "touchstone text required"
    },
    {
      "id": "match-steps",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "z_r": 2,
        "z_i": 0,
        "steps": [
          {
            "kind": "series-X",
            "x_norm": 1
          }
        ]
      },
      "expect": {
        "z_r": 2,
        "z_i": 1
      },
      "expectWarning": null,
      "actual": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "load_z_r": 2,
        "load_z_i": 0,
        "z_r": 2,
        "z_i": 1,
        "y_r": 0.4,
        "y_i": -0.2,
        "gamma_r": 0.4,
        "gamma_i": 0.2,
        "gamma_mag": 0.447213595499958,
        "gamma_angle_deg": 26.56505117707799,
        "VSWR": 2.618033988749895,
        "RL_dB": 6.9897000433601875,
        "steps": [
          {
            "index": 0,
            "kind": "series-X",
            "L_H": null,
            "C_F": null,
            "R_ohm": null,
            "n": null,
            "theta_deg": null,
            "Z0_line_ohm": null,
            "Z0_stub_ohm": null,
            "x_norm": 1,
            "b_norm": 0,
            "z_r": 2,
            "z_i": 1
          }
        ],
        "path": [
          {
            "gamma_r": 0.3333333333333333,
            "gamma_i": 0
          },
          {
            "gamma_r": 0.4,
            "gamma_i": 0.2
          }
        ],
        "matched": false,
        "note": "Looking-in after steps from load toward generator (L·C·R · tline · stub · transformer · ‖RLC). UI plots full arc path.",
        "chart_x": 352.8,
        "chart_y": 213.6
      },
      "tol": 1e-9
    },
    {
      "id": "tline-90",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "z_r": 2,
        "z_i": 0,
        "steps": [
          {
            "kind": "tline",
            "theta_deg": 90,
            "Z0_line_ohm": 50
          }
        ]
      },
      "expect": {
        "z_r": 0.5,
        "z_i": 0
      },
      "expectWarning": null,
      "actual": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "load_z_r": 2,
        "load_z_i": 0,
        "z_r": 0.5000000000000001,
        "z_i": -4.5924254968025755e-17,
        "y_r": 1.9999999999999996,
        "y_i": 1.8369701987210294e-16,
        "gamma_r": -0.33333333333333326,
        "gamma_i": -4.082155997157845e-17,
        "gamma_mag": 0.33333333333333326,
        "gamma_angle_deg": -180,
        "VSWR": 1.9999999999999998,
        "RL_dB": 9.54242509439325,
        "steps": [
          {
            "index": 0,
            "kind": "tline",
            "L_H": null,
            "C_F": null,
            "R_ohm": null,
            "n": null,
            "theta_deg": 90,
            "Z0_line_ohm": 50,
            "Z0_stub_ohm": null,
            "x_norm": 0,
            "b_norm": 0,
            "z_r": 0.5000000000000001,
            "z_i": -4.5924254968025755e-17
          }
        ],
        "path": [
          {
            "gamma_r": 0.3333333333333333,
            "gamma_i": 0
          },
          {
            "gamma_r": -0.33333333333333326,
            "gamma_i": -4.082155997157845e-17
          }
        ],
        "matched": false,
        "note": "Looking-in after steps from load toward generator (L·C·R · tline · stub · transformer · ‖RLC). UI plots full arc path.",
        "chart_x": 182.66666666666669,
        "chart_y": 260
      },
      "tol": 1e-9
    },
    {
      "id": "s11-touchstone",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "s11-touchstone",
        "touchstone": "# Hz S MA R 50\n1000000000 0.3333333333333333 0"
      },
      "expect": {
        "n": 1,
        "gamma_r": 0.3333333333333333,
        "gamma_i": 0
      },
      "expectWarning": null,
      "actual": {
        "mode": "s11-touchstone",
        "Z0_ohm": 50,
        "n": 1,
        "f_Hz": 1000000000,
        "gamma_r": 0.3333333333333333,
        "gamma_i": 0,
        "z_r": 1.9999999999999998,
        "z_i": 0,
        "y_r": 0.5000000000000001,
        "y_i": 0,
        "gamma_mag": 0.3333333333333333,
        "gamma_angle_deg": 0,
        "VSWR": 1.9999999999999998,
        "RL_dB": 9.54242509439325,
        "points": [
          {
            "f_Hz": 1000000000,
            "gamma_r": 0.3333333333333333,
            "gamma_i": 0
          }
        ],
        "note": "Parsed S11 as Γ(f). UI overlays locus on the Smith chart.",
        "chart_x": 337.3333333333333,
        "chart_y": 260
      },
      "tol": 1e-9
    },
    {
      "id": "auto-match",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "auto-match",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "z_r": 2,
        "z_i": 0,
        "topology": "l-section"
      },
      "expect": {
        "n": 2,
        "already_matched": false
      },
      "expectWarning": null,
      "actual": {
        "mode": "auto-match",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "load_z_r": 2,
        "load_z_i": 0,
        "already_matched": false,
        "solutions": [
          {
            "id": "l-shunt-series-p",
            "topology": "l-section",
            "name": "L-section shunt→series (+√)",
            "steps": [
              {
                "kind": "shunt-C",
                "C_F": 1.5915494309189534e-12
              },
              {
                "kind": "series-L",
                "L_H": 7.957747154594767e-9
              }
            ],
            "steps_norm": [
              {
                "kind": "shunt-B",
                "b_norm": 0.5
              },
              {
                "kind": "series-X",
                "x_norm": 1
              }
            ],
            "residual": 0,
            "gamma_mag": 0,
            "matched": true,
            "z_r": 1,
            "z_i": 0,
            "VSWR": 1,
            "note": "Shunt element at load, series toward generator."
          },
          {
            "id": "l-shunt-series-n",
            "topology": "l-section",
            "name": "L-section shunt→series (−√)",
            "steps": [
              {
                "kind": "shunt-L",
                "L_H": 1.5915494309189534e-8
              },
              {
                "kind": "series-C",
                "C_F": 3.1830988618379067e-12
              }
            ],
            "steps_norm": [
              {
                "kind": "shunt-B",
                "b_norm": -0.5
              },
              {
                "kind": "series-X",
                "x_norm": -1
              }
            ],
            "residual": 0,
            "gamma_mag": 0,
            "matched": true,
            "z_r": 1,
            "z_i": 0,
            "VSWR": 1,
            "note": "Shunt element at load, series toward generator."
          }
        ],
        "n": 2,
        "best": {
          "id": "l-shunt-series-p",
          "topology": "l-section",
          "name": "L-section shunt→series (+√)",
          "steps": [
            {
              "kind": "shunt-C",
              "C_F": 1.5915494309189534e-12
            },
            {
              "kind": "series-L",
              "L_H": 7.957747154594767e-9
            }
          ],
          "steps_norm": [
            {
              "kind": "shunt-B",
              "b_norm": 0.5
            },
            {
              "kind": "series-X",
              "x_norm": 1
            }
          ],
          "residual": 0,
          "gamma_mag": 0,
          "matched": true,
          "z_r": 1,
          "z_i": 0,
          "VSWR": 1,
          "note": "Shunt element at load, series toward generator."
        },
        "note": "Analytical L-section / single-stub / λ/4 candidates, verified on the match engine."
      },
      "tol": 1e-9
    },
    {
      "id": "series-R",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "z_r": 2,
        "z_i": 1,
        "steps": [
          {
            "kind": "series-R",
            "R_ohm": 10
          }
        ]
      },
      "expect": {
        "z_r": 2.2,
        "z_i": 1
      },
      "expectWarning": null,
      "actual": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "load_z_r": 2,
        "load_z_i": 1,
        "z_r": 2.2,
        "z_i": 1,
        "y_r": 0.3767123287671233,
        "y_i": -0.17123287671232876,
        "gamma_r": 0.4306049822064057,
        "gamma_i": 0.1779359430604982,
        "gamma_mag": 0.4659204336942176,
        "gamma_angle_deg": 22.45154645600387,
        "VSWR": 2.7447603806188643,
        "RL_dB": 6.6337648489431285,
        "steps": [
          {
            "index": 0,
            "kind": "series-R",
            "L_H": null,
            "C_F": null,
            "R_ohm": 10,
            "n": null,
            "theta_deg": null,
            "Z0_line_ohm": null,
            "Z0_stub_ohm": null,
            "x_norm": 0,
            "b_norm": 0,
            "z_r": 2.2,
            "z_i": 1
          }
        ],
        "path": [
          {
            "gamma_r": 0.4,
            "gamma_i": 0.2
          },
          {
            "gamma_r": 0.4306049822064057,
            "gamma_i": 0.1779359430604982
          }
        ],
        "matched": false,
        "note": "Looking-in after steps from load toward generator (L·C·R · tline · stub · transformer · ‖RLC). UI plots full arc path.",
        "chart_x": 359.9003558718861,
        "chart_y": 218.71886120996442
      },
      "tol": 1e-9
    },
    {
      "id": "transformer",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "z_r": 2,
        "z_i": 1,
        "steps": [
          {
            "kind": "transformer",
            "n": 2
          }
        ]
      },
      "expect": {
        "z_r": 0.5,
        "z_i": 0.25
      },
      "expectWarning": null,
      "actual": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "load_z_r": 2,
        "load_z_i": 1,
        "z_r": 0.5,
        "z_i": 0.25,
        "y_r": 1.6,
        "y_i": -0.8,
        "gamma_r": -0.2972972972972973,
        "gamma_i": 0.21621621621621623,
        "gamma_mag": 0.3676073110469039,
        "gamma_angle_deg": 143.9726266148964,
        "VSWR": 2.1625919067959654,
        "RL_dB": 8.69231719730976,
        "steps": [
          {
            "index": 0,
            "kind": "transformer",
            "L_H": null,
            "C_F": null,
            "R_ohm": null,
            "n": 2,
            "theta_deg": null,
            "Z0_line_ohm": null,
            "Z0_stub_ohm": null,
            "x_norm": 0,
            "b_norm": 0,
            "z_r": 0.5,
            "z_i": 0.25
          }
        ],
        "path": [
          {
            "gamma_r": 0.4,
            "gamma_i": 0.2
          },
          {
            "gamma_r": -0.2972972972972973,
            "gamma_i": 0.21621621621621623
          }
        ],
        "matched": false,
        "note": "Looking-in after steps from load toward generator (L·C·R · tline · stub · transformer · ‖RLC). UI plots full arc path.",
        "chart_x": 191.02702702702703,
        "chart_y": 209.83783783783784
      },
      "tol": 1e-9
    },
    {
      "id": "parallel-RLC",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "z_r": 2,
        "z_i": 1,
        "steps": [
          {
            "kind": "parallel-RLC",
            "R_ohm": 100,
            "L_H": 5e-9,
            "C_F": 1e-12
          }
        ]
      },
      "expect": {
        "z_r": 0.3007336194861796,
        "z_i": 0.49366765764681897
      },
      "expectWarning": null,
      "actual": {
        "mode": "match-steps",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "load_z_r": 2,
        "load_z_i": 1,
        "z_r": 0.3007336194861796,
        "z_i": 0.49366765764681897,
        "y_r": 0.9,
        "y_i": -1.477390165559974,
        "gamma_r": -0.3439998612125404,
        "gamma_i": 0.510088501921353,
        "gamma_mag": 0.6152448165621691,
        "gamma_angle_deg": 123.99543115110852,
        "VSWR": 4.198110606671429,
        "RL_dB": 4.219040730818683,
        "steps": [
          {
            "index": 0,
            "kind": "parallel-RLC",
            "L_H": 5e-9,
            "C_F": 1e-12,
            "R_ohm": 100,
            "n": null,
            "theta_deg": null,
            "Z0_line_ohm": null,
            "Z0_stub_ohm": null,
            "x_norm": 0,
            "b_norm": -1.277390165559974,
            "z_r": 0.3007336194861796,
            "z_i": 0.49366765764681897
          }
        ],
        "path": [
          {
            "gamma_r": 0.4,
            "gamma_i": 0.2
          },
          {
            "gamma_r": -0.3439998612125404,
            "gamma_i": 0.510088501921353
          }
        ],
        "matched": false,
        "note": "Looking-in after steps from load toward generator (L·C·R · tline · stub · transformer · ‖RLC). UI plots full arc path.",
        "chart_x": 180.19203219869064,
        "chart_y": 141.6594675542461
      },
      "tol": 1e-9
    },
    {
      "id": "boundary-smith-s11",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "s11-touchstone",
        "touchstone": "# Hz S MA R 50\n1e9 0.3333333333333333 0"
      },
      "expect": {
        "n": 1,
        "gamma_r": 0.3333333333333333
      },
      "expectWarning": null,
      "actual": {
        "mode": "s11-touchstone",
        "Z0_ohm": 50,
        "n": 1,
        "f_Hz": 1000000000,
        "gamma_r": 0.3333333333333333,
        "gamma_i": 0,
        "z_r": 1.9999999999999998,
        "z_i": 0,
        "y_r": 0.5000000000000001,
        "y_i": 0,
        "gamma_mag": 0.3333333333333333,
        "gamma_angle_deg": 0,
        "VSWR": 1.9999999999999998,
        "RL_dB": 9.54242509439325,
        "points": [
          {
            "f_Hz": 1000000000,
            "gamma_r": 0.3333333333333333,
            "gamma_i": 0
          }
        ],
        "note": "Parsed S11 as Γ(f). UI overlays locus on the Smith chart.",
        "chart_x": 337.3333333333333,
        "chart_y": 260
      },
      "tol": 1e-9
    },
    {
      "id": "boundary-smith-auto",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "auto-match",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "z_r": 2,
        "z_i": 0,
        "topology": "l-section"
      },
      "expect": {
        "n": 2
      },
      "expectWarning": null,
      "actual": {
        "mode": "auto-match",
        "Z0_ohm": 50,
        "f_Hz": 1000000000,
        "load_z_r": 2,
        "load_z_i": 0,
        "already_matched": false,
        "solutions": [
          {
            "id": "l-shunt-series-p",
            "topology": "l-section",
            "name": "L-section shunt→series (+√)",
            "steps": [
              {
                "kind": "shunt-C",
                "C_F": 1.5915494309189534e-12
              },
              {
                "kind": "series-L",
                "L_H": 7.957747154594767e-9
              }
            ],
            "steps_norm": [
              {
                "kind": "shunt-B",
                "b_norm": 0.5
              },
              {
                "kind": "series-X",
                "x_norm": 1
              }
            ],
            "residual": 0,
            "gamma_mag": 0,
            "matched": true,
            "z_r": 1,
            "z_i": 0,
            "VSWR": 1,
            "note": "Shunt element at load, series toward generator."
          },
          {
            "id": "l-shunt-series-n",
            "topology": "l-section",
            "name": "L-section shunt→series (−√)",
            "steps": [
              {
                "kind": "shunt-L",
                "L_H": 1.5915494309189534e-8
              },
              {
                "kind": "series-C",
                "C_F": 3.1830988618379067e-12
              }
            ],
            "steps_norm": [
              {
                "kind": "shunt-B",
                "b_norm": -0.5
              },
              {
                "kind": "series-X",
                "x_norm": -1
              }
            ],
            "residual": 0,
            "gamma_mag": 0,
            "matched": true,
            "z_r": 1,
            "z_i": 0,
            "VSWR": 1,
            "note": "Shunt element at load, series toward generator."
          }
        ],
        "n": 2,
        "best": {
          "id": "l-shunt-series-p",
          "topology": "l-section",
          "name": "L-section shunt→series (+√)",
          "steps": [
            {
              "kind": "shunt-C",
              "C_F": 1.5915494309189534e-12
            },
            {
              "kind": "series-L",
              "L_H": 7.957747154594767e-9
            }
          ],
          "steps_norm": [
            {
              "kind": "shunt-B",
              "b_norm": 0.5
            },
            {
              "kind": "series-X",
              "x_norm": 1
            }
          ],
          "residual": 0,
          "gamma_mag": 0,
          "matched": true,
          "z_r": 1,
          "z_i": 0,
          "VSWR": 1,
          "note": "Shunt element at load, series toward generator."
        },
        "note": "Analytical L-section / single-stub / λ/4 candidates, verified on the match engine."
      },
      "tol": 1e-9
    },
    {
      "id": "boundary-smith-ts-v2",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "s11-touchstone",
        "touchstone": "[Version] 2.0\n# Hz S MA R 50\n1e9 0.3 0"
      },
      "expectError": "TOUCHSTONE_UNSUPPORTED_FORMAT",
      "code": "TOUCHSTONE_UNSUPPORTED_FORMAT",
      "error": "Touchstone 2.x keyword sections are not supported in s11-touchstone"
    },
    {
      "id": "property-matched",
      "ok": true,
      "kind": "property",
      "detail": "0",
      "expect": 0,
      "actual": 0
    },
    {
      "id": "property-steps-x",
      "ok": true,
      "kind": "property",
      "detail": "z_i=1",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-tline-90",
      "ok": true,
      "kind": "property",
      "detail": "z_r=0.5",
      "expect": 0.5,
      "actual": 0.5000000000000001
    },
    {
      "id": "property-auto-n",
      "ok": true,
      "kind": "property",
      "detail": "n≥2",
      "expect": 2,
      "actual": 2
    },
    {
      "id": "property-auto-best",
      "ok": true,
      "kind": "property",
      "detail": "residual≈0",
      "expect": 0,
      "actual": 0
    },
    {
      "id": "property-series-R",
      "ok": true,
      "kind": "property",
      "detail": "z_r=2.2",
      "expect": 2.2,
      "actual": 2.2
    },
    {
      "id": "property-transformer",
      "ok": true,
      "kind": "property",
      "detail": "z=0.5+j0.25",
      "expect": "0.5+j0.25",
      "actual": "0.5+j0.25"
    }
  ],
  "tier": "internally_reviewed",
  "verification": {
    "tests": {
      "passed": 21,
      "total": 21,
      "golden": 9,
      "boundary": 5,
      "property": 7
    },
    "contract_checks": {
      "passed": 8,
      "total": 8
    }
  },
  "evidence_core_generated_at": "2026-09-08T06:02:05.651Z",
  "rendered_at": "2026-09-16T22:03:43.750Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.6.3",
    "artifacts": {
      "engine": "1.6.3",
      "page": "1.6.3",
      "capability": "1.6.3",
      "evidence": "1.6.3",
      "input_schema": "1.6.3",
      "output_schema": "1.6.3",
      "mcp_contract": "1.6.3"
    },
    "digests": {
      "input_schema_sha256": "a05ef25ca7cf35bc01f6722b882e746a008756fc0dd54724052d34e5ddac35b7",
      "output_schema_sha256": "5736600d32f028e3ae48b600659781b97c032b017db38f2bb489284177b06234",
      "evidence_sha256": "224baa42ce2b6874dee338b6fb794d58b938e975cdaf091c720cea4a4fffd8a0",
      "evidence_core_sha256": "224baa42ce2b6874dee338b6fb794d58b938e975cdaf091c720cea4a4fffd8a0",
      "capability_sha256": "cc480f3041cdc51ec038c3192dea66bc60373230f16c5516610d0b88b6f5b93f",
      "engine_sha256": "c8d4ccdbfeaf61d7b024d4e1babb0c2ba3b324c1b37bd0cb456a526d8d2b1bd1",
      "mcp_contract_sha256": "863098b311a7b17dc4b229a6302b90b3545b175f716e5d84772c7be8e9716b86"
    },
    "contract_checks": {
      "total": 8,
      "passed": 8,
      "failed": 0,
      "items": [
        {
          "id": "contract-page-version",
          "status": "pass",
          "detail": "1.6.3"
        },
        {
          "id": "contract-capability-version",
          "status": "pass",
          "detail": "1.6.3"
        },
        {
          "id": "contract-input-schema-version",
          "status": "pass",
          "detail": "1.6.3"
        },
        {
          "id": "contract-output-schema-version",
          "status": "pass",
          "detail": "1.6.3"
        },
        {
          "id": "evidence-version-matches-manifest",
          "status": "pass",
          "detail": "1.6.3"
        },
        {
          "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"
  }
}