{
  "outcome": "passes Hamdi's passive cylinder challenge; official excited-mode response-sign confirmation remains a stated caveat",
  "model_scope": "three-angular-DOF reduced rotational model; translational MBS dynamics and rotation-translation feedback are neglected",
  "central_candidate": {
    "spin_acceleration_rad_s2": 0.0,
    "field_frequency_hz": 60.0,
    "magnetic_coupling_J": 0.002184760832934153,
    "field_tilt_deg": 4.570078733480211,
    "damping_per_s": 0.0982787764237392,
    "uniform_axisymmetric_cylinder": true,
    "height_over_diameter": 0.5125605301591867,
    "principal_moments_kg_m2": [
      1.0e-7,
      1.0e-7,
      1.481162139885631e-7
    ],
    "manufacturing_magnetic_axis_tilt_deg": 5.476228447888703,
    "manufacturing_tilt_azimuth_deg": 135.23482434892398
  },
  "strict_numerics": {
    "duration_s": 200.0,
    "saved_samples_per_s": 2500.0,
    "solver": "LSODA",
    "relative_tolerance": 1.0e-10,
    "absolute_tolerance": 1.0e-12,
    "maximum_step_s": 0.00020833333333333335,
    "minimum_internal_steps_per_drive_period": 80
  },
  "self_spin_up": {
    "initial_physical_cylinder_axis_spin_rad_s": 7.456671213808739e-16,
    "mean_spin_0_to_0p5_s_rad_s": -9.24991415639672,
    "mean_spin_0p5_to_2_s_rad_s": -16.59059841485554,
    "mean_spin_120_to_200_s_rad_s": -6.783500882357006,
    "interpretation": "The physical cylinder-axis spin starts at numerical zero and develops dynamically under the rotating-field drive, settling counter to the positive field rotation. No imposed spin acceleration is present."
  },
  "excited_branch_120_to_200_s": {
    "theta_mean_deg": 103.46877392603706,
    "theta_span_deg": 147.15008930724917,
    "physical_spin_mean_rad_s": -6.783500882357006,
    "potential_over_mB_mean": 0.148042232133819,
    "mean_total_energy_J": 0.0009283906699041214,
    "field_power_mean_W": 0.00011882234933431779,
    "damping_loss_mean_W": 0.00011892088967058475,
    "mechanical_energy_change_rate_W": -9.812257632026166e-8,
    "energy_power_closure_error_W": 4.177599467042639e-10
  },
  "excited_branch_180_to_200_s": {
    "theta_mean_deg": 103.46796888805427,
    "theta_min_deg": 31.52547708346716,
    "theta_max_deg": 178.42741124821472,
    "theta_span_deg": 146.90193416474756,
    "physical_spin_mean_rad_s": -6.784000307965255,
    "physical_spin_standard_deviation_rad_s": 2.5074378039991334,
    "potential_over_mB_mean": 0.14803750444089203,
    "potential_positive_fraction": 0.6714865702685946,
    "mean_total_energy_J": 0.0009284282694887652
  },
  "matched_regular_cone_180_to_200_s": {
    "theta_mean_deg": 8.912548279802287,
    "theta_span_deg": 0.05091301776122492,
    "potential_over_mB_mean": 0.07571767336523709,
    "mean_total_energy_J": 0.00033624031685777387
  },
  "matched_comparison": {
    "excited_to_cone_mean_energy_ratio": 2.761091229278422,
    "excited_minus_cone_mean_energy_J": 0.0005921501791664266,
    "large_theta_requirement_passed": true,
    "regular_fixed_theta_below_15deg_passed": true,
    "nonzero_damping_200s_passed": true,
    "zero_control_and_self_spin_up_passed": true
  },
  "standard_perturbation_recovery": {
    "angle_delta_deg": [0.2, -0.15, 0.1],
    "rate_delta_rad_s": [0.05, -0.04, 0.03],
    "late_theta_mean_difference_deg": -0.007847427962119014,
    "late_theta_span_difference_deg": -0.0031010671173987703,
    "late_spin_mean_difference_rad_s": 0.0005967496324119637,
    "late_total_energy_relative_difference": 0.00029275978810753634,
    "same_branch_recovered": true
  },
  "eight_second_cross_solver": {
    "LSODA_vs_DOP853_theta_max_difference_deg": 9.772530660256962e-7,
    "LSODA_vs_DOP853_body_omega_max_difference_rad_s": 2.5416648514822216e-6,
    "LSODA_vs_DOP853_quaternion_geodesic_max_rad": 5.960464477539063e-8,
    "passed": true
  },
  "response_sign_caveat": {
    "source": "../passive_cylinder_index19_mb_response.json",
    "mB_continuation_excited_theta_mean_slope_deg_per_rad_s": 2.824180065501267,
    "mB_continuation_excited_theta_span_slope_deg_per_rad_s": -2.2549092870251517,
    "mB_continuation_cone_theta_mean_slope_deg_per_rad_s": 23.920151988709623,
    "interpretation": "The mB sweep gives the desired opposite sign for theta amplitude/span, but not for mean theta. Because mB and selected spin both change, this is not a clean fixed-parameter physical-spin continuation. Treat the branch as a fully verified solution to the stated challenge and a strong stable angular excited candidate; reserve the most stringent official excited-mode label until a clean inverse mean-theta/spin diagnostic is agreed or demonstrated."
  }
}