{
  "version": "2026-09-07",
  "scope": "Selected numerical controls and explicit adverse inputs; not verification of every claim in the guide.",
  "started_utc": "2026-09-07T07:29:38.075249+00:00",
  "environment": {
    "python": "3.12.9",
    "platform": "macOS-26.6.2-arm64-arm-64bit",
    "packages": {
      "mpmath": {
        "expected": "1.3.0",
        "actual": "1.3.0"
      },
      "numpy": {
        "expected": "2.0.2",
        "actual": "2.0.2"
      },
      "scipy": {
        "expected": "1.13.1",
        "actual": "1.13.1"
      },
      "sympy": {
        "expected": "1.14.0",
        "actual": "1.14.0"
      }
    },
    "differences": []
  },
  "manifest_sha256": "ccdcd032c6bfc0fe2cdee79066640e79cbb65812676748019f345bf4b9f2048c",
  "cases": [
    {
      "id": "gauss",
      "purpose": "Connection coefficients, Abel identity, ODE residual, and basis phase at three points",
      "page": "/advanced-ode/start-here/gauss-connection/",
      "command": [
        "python",
        "gauss-starter-check.py",
        "--json"
      ],
      "expected_exit": 0,
      "source_sha256": "b6c340a02891e08cd495c647c14b1ebeda4ccbfb494a5465160c24fb87db32e4",
      "exit": 0,
      "stdout": "{\n  \"status\": \"PASS\",\n  \"terms\": 240,\n  \"dps\": 60,\n  \"tolerance\": \"1.0e-30\",\n  \"reference_A\": \"1.16278702942702179\",\n  \"reference_B\": \"-0.375\",\n  \"maximum_checked_error\": \"8.4508284e-41\",\n  \"match_points\": [\n    {\n      \"z\": \"0.333333333333\",\n      \"A\": \"1.16278702942702179\",\n      \"B\": \"-0.375\",\n      \"coefficient_relative_error\": \"8.5519947e-43\",\n      \"abel_relative_error\": \"1.5756177e-42\",\n      \"ode_scaled_residual\": \"8.4508284e-41\",\n      \"basis_phase_error\": \"3.1346632e-61\"\n    },\n    {\n      \"z\": \"0.5\",\n      \"A\": \"1.16278702942702179\",\n      \"B\": \"-0.375\",\n      \"coefficient_relative_error\": \"3.1115076e-61\",\n      \"abel_relative_error\": \"2.3336307e-61\",\n      \"ode_scaled_residual\": \"6.6933164e-62\",\n      \"basis_phase_error\": \"2.0593737e-62\"\n    },\n    {\n      \"z\": \"0.666666666667\",\n      \"A\": \"1.16278702942702179\",\n      \"B\": \"-0.375\",\n      \"coefficient_relative_error\": \"1.0935294e-44\",\n      \"abel_relative_error\": \"0.0\",\n      \"ode_scaled_residual\": \"4.0415898e-43\",\n      \"basis_phase_error\": \"7.9553388e-62\"\n    }\n  ]\n}\n",
      "stderr": "",
      "scientific_status": "PASS",
      "elapsed_seconds": 0.085,
      "test_status": "PASS"
    },
    {
      "id": "gauss-underresolved",
      "purpose": "Insufficient series order must be rejected",
      "page": "/advanced-ode/start-here/gauss-connection/",
      "command": [
        "python",
        "gauss-starter-check.py",
        "--terms",
        "24",
        "--json"
      ],
      "expected_exit": 1,
      "source_sha256": "b6c340a02891e08cd495c647c14b1ebeda4ccbfb494a5465160c24fb87db32e4",
      "exit": 1,
      "stdout": "{\n  \"status\": \"FAIL\",\n  \"terms\": 24,\n  \"dps\": 60,\n  \"tolerance\": \"1.0e-30\",\n  \"reference_A\": \"1.16278702942702179\",\n  \"reference_B\": \"-0.375\",\n  \"maximum_checked_error\": \"0.0005176834\",\n  \"match_points\": [\n    {\n      \"z\": \"0.333333333333\",\n      \"A\": \"1.16276842844700104\",\n      \"B\": \"-0.374980883162825697\",\n      \"coefficient_relative_error\": \"5.0978232e-5\",\n      \"abel_relative_error\": \"9.9821721e-5\",\n      \"ode_scaled_residual\": \"0.0005176834\",\n      \"basis_phase_error\": \"1.6465599e-62\"\n    },\n    {\n      \"z\": \"0.5\",\n      \"A\": \"1.16278700125981103\",\n      \"B\": \"-0.374999961762260758\",\n      \"coefficient_relative_error\": \"1.019673e-7\",\n      \"abel_relative_error\": \"1.062737e-7\",\n      \"ode_scaled_residual\": \"1.1011029e-6\",\n      \"basis_phase_error\": \"4.3180878e-62\"\n    },\n    {\n      \"z\": \"0.666666666667\",\n      \"A\": \"1.16278589883546727\",\n      \"B\": \"-0.374998029237277551\",\n      \"coefficient_relative_error\": \"5.2553673e-6\",\n      \"abel_relative_error\": \"6.5751093e-12\",\n      \"ode_scaled_residual\": \"2.0282694e-5\",\n      \"basis_phase_error\": \"1.5855687e-62\"\n    }\n  ]\n}\n",
      "stderr": "",
      "scientific_status": "FAIL",
      "elapsed_seconds": 0.054,
      "test_status": "PASS"
    },
    {
      "id": "weber",
      "purpose": "Exact Wronskian and independently refined finite-difference spectrum",
      "page": "/advanced-ode/start-here/weber-spectrum/",
      "command": [
        "python",
        "weber-starter-check.py",
        "--json"
      ],
      "expected_exit": 0,
      "source_sha256": "69b52074ff4bfd74126e4921e2d14caed4148803d2004f6a2a4957e89b62a40e",
      "exit": 0,
      "stdout": "{\n  \"status\": \"PASS\",\n  \"hbar\": \"1.0\",\n  \"half_width_in_oscillator_lengths\": 8.0,\n  \"grid_intervals\": [\n    1200,\n    2400,\n    4800\n  ],\n  \"tolerance_in_hbar_units\": 2e-07,\n  \"wronskian_checks\": [\n    {\n      \"E_over_hbar\": \"0\",\n      \"scaled_wronskian_error\": \"8.9092157e-52\"\n    },\n    {\n      \"E_over_hbar\": \"1.4\",\n      \"scaled_wronskian_error\": \"8.3058227e-52\"\n    },\n    {\n      \"E_over_hbar\": \"2.5\",\n      \"scaled_wronskian_error\": \"7.7100207e-52\"\n    },\n    {\n      \"E_over_hbar\": \"6.2\",\n      \"scaled_wronskian_error\": \"1.0714775e-51\"\n    }\n  ],\n  \"grid_spectra_in_hbar_units\": [\n    [\n      0.9999888887648858,\n      2.999944443334502,\n      4.999855551233039,\n      6.999722210987527\n    ],\n    [\n      0.9999972222109081,\n      2.999986111039895,\n      4.999963888626226,\n      6.999930554849909\n    ],\n    [\n      0.9999993055773935,\n      2.99999652778056,\n      4.999990972212403,\n      6.999982638872925\n    ]\n  ],\n  \"richardson_spectrum_in_hbar_units\": [\n    1.0000000000328886,\n    3.0000000000274483,\n    5.000000000074462,\n    7.00000000021393\n  ],\n  \"exact_spectrum_in_hbar_units\": [\n    1.0,\n    3.0,\n    5.0,\n    7.0\n  ],\n  \"maximum_spectral_error\": 2.1393020688265096e-10,\n  \"richardson_refinement_change\": 2.590105907529505e-09,\n  \"endpoint_refinement_change\": 6.454958789703369e-11\n}\n",
      "stderr": "",
      "scientific_status": "PASS",
      "elapsed_seconds": 1.67,
      "test_status": "PASS"
    },
    {
      "id": "weber-wrong-domain",
      "purpose": "An inadequate endpoint distance must fail the spectral comparison",
      "page": "/advanced-ode/start-here/weber-spectrum/",
      "command": [
        "python",
        "weber-starter-check.py",
        "--half-width",
        "2",
        "--json"
      ],
      "expected_exit": 1,
      "source_sha256": "69b52074ff4bfd74126e4921e2d14caed4148803d2004f6a2a4957e89b62a40e",
      "exit": 1,
      "stdout": "{\n  \"status\": \"FAIL\",\n  \"hbar\": \"1.0\",\n  \"half_width_in_oscillator_lengths\": 2.0,\n  \"grid_intervals\": [\n    1200,\n    2400,\n    4800\n  ],\n  \"tolerance_in_hbar_units\": 2e-07,\n  \"wronskian_checks\": [\n    {\n      \"E_over_hbar\": \"0\",\n      \"scaled_wronskian_error\": \"8.9092157e-52\"\n    },\n    {\n      \"E_over_hbar\": \"1.4\",\n      \"scaled_wronskian_error\": \"8.3058227e-52\"\n    },\n    {\n      \"E_over_hbar\": \"2.5\",\n      \"scaled_wronskian_error\": \"7.7100207e-52\"\n    },\n    {\n      \"E_over_hbar\": \"6.2\",\n      \"scaled_wronskian_error\": \"1.0714775e-51\"\n    }\n  ],\n  \"grid_spectra_in_hbar_units\": [\n    [\n      1.0749217517714826,\n      3.529626489572658,\n      6.79954710528412,\n      11.169187190880324\n    ],\n    [\n      1.074922252006135,\n      3.5296312805185144,\n      6.799569138017372,\n      11.169255416317835\n    ],\n    [\n      1.0749223769077823,\n      3.529632478483618,\n      6.799574646758238,\n      11.169272472315171\n    ]\n  ],\n  \"richardson_spectrum_in_hbar_units\": [\n    1.0749224185416646,\n    3.5296328778053194,\n    6.799576483005193,\n    11.169278157647616\n  ],\n  \"exact_spectrum_in_hbar_units\": [\n    1.0,\n    3.0,\n    5.0,\n    7.0\n  ],\n  \"maximum_spectral_error\": 4.169278157647616,\n  \"richardson_refinement_change\": 7.434044491105851e-10,\n  \"endpoint_refinement_change\": 2.8007555204380115\n}\n",
      "stderr": "",
      "scientific_status": "FAIL",
      "elapsed_seconds": 1.628,
      "test_status": "PASS"
    },
    {
      "id": "heun",
      "purpose": "Both Abel determinants and full connection-matrix drift",
      "page": "/advanced-ode/reference/appendix-c-computational-laboratory/#a-quick-connection-matrix-micro-lab",
      "command": [
        "python",
        "general-heun-connection-check.py",
        "--no-table",
        "--verify"
      ],
      "expected_exit": 0,
      "source_sha256": "5675e36730d49f9cb9218421b50b76173910ef351e91c99e4a9fa2799ea8b5bc",
      "exit": 0,
      "stdout": "t=0.04, order=2, terms=120\ndirect Frobenius matrix\n  0.6852083269293459  0.5321827959047746\n  1.047109773636109  -0.6945959089055297\nclassical-block matrix\n  0.6852142054292528  0.5321841142916558\n  1.047098391355132  -0.6945967754832237\nmaximum relative entry error = 1.0870188841823e-5\n  (finite-order block comparison; excluded from verification)\ndeterminants (direct, block, Abel) = -1.03319670758600654, -1.03319670758600654, -1.03319670758600654\n\nmaximum relative change between z=t/2 and z=t/3 = 2.2798812124209e-22\n\nNumerical checks (errors scaled by max(1, |reference|)); tolerance = 1.0e-12\n  PASS: Abel determinant at z=t/2 = 3.0381862002693e-39\n  PASS: Abel determinant at z=t/3 = 1.598258677289e-22\n  PASS: two-point matrix drift = 1.5835961629381e-22\nverification: PASS\n",
      "stderr": "",
      "elapsed_seconds": 0.076,
      "test_status": "PASS"
    },
    {
      "id": "heun-underresolved",
      "purpose": "Matrix error is detected even when a determinant alone appears converged",
      "page": "/advanced-ode/study-paths/#route-a-analytic-connection-methods",
      "command": [
        "python",
        "general-heun-connection-check.py",
        "--t",
        "0.04",
        "--terms",
        "24",
        "--dps",
        "50",
        "--no-table",
        "--verify"
      ],
      "expected_exit": 1,
      "source_sha256": "5675e36730d49f9cb9218421b50b76173910ef351e91c99e4a9fa2799ea8b5bc",
      "exit": 1,
      "stdout": "t=0.04, order=2, terms=24\ndirect Frobenius matrix\n  0.685208335509995  0.532182798236554\n  1.047109746507397  -0.6945959170766861\nclassical-block matrix\n  0.6852142054292528  0.5321841142916558\n  1.047098391355132  -0.6945967754832237\nmaximum relative entry error = 1.0844280938967e-5\n  (finite-order block comparison; excluded from verification)\ndeterminants (direct, block, Abel) = -1.03319670714922966, -1.03319670758600654, -1.03319670758600654\n\nmaximum relative change between z=t/2 and z=t/3 = 3.0840638920608e-5\n\nNumerical checks (errors scaled by max(1, |reference|)); tolerance = 1.0e-12\n  FAIL: Abel determinant at z=t/2 = 4.2274320167639e-10\n  FAIL: Abel determinant at z=t/3 = 2.144021116614e-5\n  FAIL: two-point matrix drift = 2.1421781874291e-5\nverification: FAIL\nRefine --terms or move farther inside the convergence disks.\n",
      "stderr": "",
      "elapsed_seconds": 0.057,
      "test_status": "PASS"
    },
    {
      "id": "heun-invalid-match",
      "purpose": "Reject a second point outside the Frobenius convergence disc",
      "page": "/advanced-ode/reference/appendix-c-computational-laboratory/",
      "command": [
        "python",
        "general-heun-connection-check.py",
        "--t",
        "0.66",
        "--no-table",
        "--check-second-point"
      ],
      "expected_exit": 2,
      "source_sha256": "5675e36730d49f9cb9218421b50b76173910ef351e91c99e4a9fa2799ea8b5bc",
      "exit": 2,
      "stdout": "",
      "stderr": "usage: general-heun-connection-check.py [-h] [--t T] [--order {0,1,2}]\n                                        [--terms TERMS] [--dps DPS]\n                                        [--no-table] [--show-ablation]\n                                        [--check-second-point] [--verify]\n                                        [--tolerance TOLERANCE]\n                                        [--show-reverse]\ngeneral-heun-connection-check.py: error: matching at z=t/3 requires 0 < t < 3/5: its distance 2*t/3 from t must be smaller than the Frobenius radius min(t, 1-t); more terms cannot repair an invalid match point\n",
      "elapsed_seconds": 0.048,
      "test_status": "PASS"
    }
  ],
  "artifact_sha256": {
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  },
  "requirements_sha256": "9ff319803ba4e78f8ba0dd99657578ced556d8fc4685424086ca8de2548fdb72",
  "status": "PASS"
}