{
  "accepted_steps": 4,
  "attempted_steps": 4,
  "elapsed_seconds": 117.65745206999964,
  "evidence_level": "cross-basis candidate; full-vector 3D validation required",
  "final": {
    "air_gap_energy_fraction": 0.22450950839111028,
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    "mode_overlap": 0.9961259162712984,
    "nonlinear_iterations": 15.0,
    "nonlinear_residual": 5.014977858770892e-09,
    "pole_imag": -0.01600459344229371,
    "pole_real": 1.0600101554588557,
    "q": 33.115810135410086
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  "fourier_harmonics": 189,
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    "air_gap_energy_fraction": 0.3118920871657279,
    "frequency": 1.0461658217029564,
    "inner_energy_fraction": 0.6956770437825058,
    "mode_overlap": 1.0,
    "nonlinear_iterations": 17.0,
    "nonlinear_residual": 4.507792593428346e-09,
    "pole_imag": -0.03406976324563698,
    "pole_real": 1.0461658217029564,
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  "invariants": {
    "maximum_density": 1.0,
    "maximum_density_in_air_strip": 0.0,
    "minimum_density": 0.0,
    "reflection_symmetry_error": 7.771561172376096e-16
  },
  "model": "scalar Fourier-Galerkin 2.5D with exact vertical DtN",
  "q_gain": 2.156919653835215,
  "unknowns": 1701
}