{
  "schema": "classical-reconstruction-hydrogen-phase-closure/v1",
  "status": "GROSS_STRUCTURE_PHASE_CLOSURE_ONLY",
  "model": {
    "ontology": "continuous real phase field on a classical Coulomb two-body orbit",
    "boundary_condition": "single-valued phase around closed orbit gives integer winding n",
    "dispersion_assumptions": [
      "p=S*k",
      "E=S*omega"
    ],
    "derived_relations": [
      "m_red*v*r=n*S",
      "r_n=n^2*S^2/(m_red*k_c*e^2)",
      "E_n=-m_red*k_c^2*e^4/(2*S^2*n^2)"
    ]
  },
  "calibration": {
    "training_line": "H-alpha n=3->2 only",
    "R_from_training_cm-1": 109709.43760199548,
    "action_scale_S_Js": 1.0544697425848603e-34,
    "S_over_hbar": 0.9999032071030269
  },
  "holdout": {
    "n_values": [
      4,
      5,
      6,
      7,
      8,
      9,
      10
    ],
    "rmse_cm-1": 0.04929773047653496,
    "max_abs_z": 1.62499613744472,
    "predictions": [
      {
        "n": 4,
        "observed_wavelength_nm": 486.135,
        "uncertainty_nm": 0.005,
        "observed_wavenumber_cm-1": 20570.41768233104,
        "predicted_wavenumber_cm-1": 20570.519550374152,
        "residual_cm-1": 0.10186804311160813,
        "z": 0.48148386583903163,
        "training_point": false
      },
      {
        "n": 5,
        "observed_wavelength_nm": 434.0472,
        "uncertainty_nm": 0.0006,
        "observed_wavenumber_cm-1": 23038.9690337825,
        "predicted_wavenumber_cm-1": 23038.98189641905,
        "residual_cm-1": 0.012862636547652073,
        "z": 0.4038802958832921,
        "training_point": false
      },
      {
        "n": 6,
        "observed_wavelength_nm": 410.1734,
        "uncertainty_nm": 0.0006,
        "observed_wavenumber_cm-1": 24379.932974688265,
        "predicted_wavenumber_cm-1": 24379.87502266566,
        "residual_cm-1": -0.057952022605604725,
        "z": -1.62499613744472,
        "training_point": false
      },
      {
        "n": 7,
        "observed_wavelength_nm": 397.0075,
        "uncertainty_nm": 0.0006,
        "observed_wavenumber_cm-1": 25188.441024413896,
        "predicted_wavenumber_cm-1": 25188.39128617243,
        "residual_cm-1": -0.04973824146509287,
        "z": -1.3065817821829209,
        "training_point": false
      },
      {
        "n": 8,
        "observed_wavelength_nm": 388.9064,
        "uncertainty_nm": 0.0006,
        "observed_wavenumber_cm-1": 25713.127888869916,
        "predicted_wavenumber_cm-1": 25713.14943796769,
        "residual_cm-1": 0.021549097775277914,
        "z": 0.5432103317840568,
        "training_point": false
      },
      {
        "n": 9,
        "observed_wavelength_nm": 383.5397,
        "uncertainty_nm": 0.0006,
        "observed_wavenumber_cm-1": 26072.920221817978,
        "predicted_wavenumber_cm-1": 26072.921899239667,
        "residual_cm-1": 0.0016774216892372351,
        "z": 0.04112554366689727,
        "training_point": false
      },
      {
        "n": 10,
        "observed_wavelength_nm": 379.7909,
        "uncertainty_nm": 0.0006,
        "observed_wavenumber_cm-1": 26330.27805563535,
        "predicted_wavenumber_cm-1": 26330.265024478915,
        "residual_cm-1": -0.013031156435317826,
        "z": -0.31327144996043277,
        "training_point": false
      }
    ]
  },
  "unpaid_physics": [
    "The phase-field dispersion p=S*k and E=S*omega is assumed, not derived from Maxwell-Lorentz matter dynamics.",
    "No dynamical attractor/stability mechanism selects or preserves the winding modes against Larmor radiation.",
    "Fine structure, Stark/Zeeman splitting, selection rules, intensities and lifetimes are not derived.",
    "One H-alpha line fixes the action scale before the other Balmer lines are predicted."
  ],
  "scope_exclusion": "Integer winding is a classical field boundary condition, but this is not yet a self-consistent classical atom. It is a gross-structure candidate showing exactly which non-quantized assumptions can generate the inverse-square series."
}