{
  "model": "Published two-mode ODE; radial saturation approximation; no full-body contact solver.",
  "calibration_SI": {
    "inertia_kg_m2": 0.0001,
    "stiffness_Nm_per_rad": 0.048,
    "damping_Nm_s_per_rad": 0.0004,
    "torque_cap_Nm": 0.004,
    "note": "4 mNm setting for the single-cell oscillation analysis, not the 12 mNm motor maximum"
  },
  "dimensionless": {
    "Gamma": 0.18257418583505539,
    "cap": 0.08333333333333333,
    "time_unit_s": 0.04564354645876384,
    "loaded_example": "load=0.2 and nu=0.1 are illustrative reduced-mode values, not a fit to the ring"
  },
  "regimes": {
    "weak_unloaded": {
      "nu": 0.1,
      "load": 0.0,
      "cap": null,
      "duration": 800.0,
      "left_small_deformation_range": false,
      "mean_radius": 2.725336182630659e-14,
      "radius_std": 4.812622475466575e-14,
      "steady_cycle": false,
      "angular_frequency": null,
      "active_power_mean": 0.0,
      "dissipated_power_mean": 0.0,
      "energy_balance_max_error": 1.416741378346912e-15
    },
    "weak_loaded": {
      "nu": 0.1,
      "load": 0.2,
      "cap": null,
      "duration": 800.0,
      "left_small_deformation_range": false,
      "mean_radius": 0.28571428571424196,
      "radius_std": 9.452090327936918e-14,
      "steady_cycle": true,
      "angular_frequency": 0.547722557505175,
      "active_power_mean": 0.004471204551063186,
      "dissipated_power_mean": 0.0044712045510631815,
      "energy_balance_max_error": 4.1300296516055823e-14
    },
    "strong_saturated": {
      "nu": 0.26,
      "load": 0.0,
      "cap": 0.08333333333333333,
      "duration": 800.0,
      "left_small_deformation_range": false,
      "mean_radius": 0.45643546458768014,
      "radius_std": 3.0808490231372367e-13,
      "steady_cycle": true,
      "angular_frequency": 0.9999999999998389,
      "active_power_mean": 0.0380362887156508,
      "dissipated_power_mean": 0.0380362887156509,
      "energy_balance_max_error": 3.524291969370097e-12
    },
    "strong_reversed": {
      "nu": -0.26,
      "load": 0.0,
      "cap": 0.08333333333333333,
      "duration": 800.0,
      "left_small_deformation_range": false,
      "mean_radius": 0.456435464587342,
      "radius_std": 8.687360892664012e-13,
      "steady_cycle": true,
      "angular_frequency": -0.999999999999839,
      "active_power_mean": 0.0380362887156509,
      "dissipated_power_mean": 0.03803628871565115,
      "energy_balance_max_error": 3.701927653310122e-12
    },
    "strong_unsaturated": {
      "nu": 0.26,
      "load": 0.0,
      "cap": null,
      "duration": 126.8458432410691,
      "left_small_deformation_range": true,
      "mean_radius": 0.8701960692719716,
      "radius_std": 0.3013687414738495,
      "steady_cycle": false,
      "angular_frequency": null,
      "active_power_mean": 0.22111216818969537,
      "dissipated_power_mean": 0.15614480241784426,
      "energy_balance_max_error": 5.5209170568559784e-12
    }
  },
  "transverse_stability_eigenvalues": {
    "loaded": [
      [
        0.0,
        0.0
      ],
      [
        -0.06679292150302359,
        0.0
      ],
      [
        -0.14917772508354343,
        1.375191371231372
      ],
      [
        -0.14917772508354343,
        -1.375191371231372
      ]
    ],
    "saturated": [
      [
        0.0,
        0.0
      ],
      [
        -0.09109651526779274,
        0.0
      ],
      [
        -0.13702592820115894,
        1.9973963200158908
      ],
      [
        -0.13702592820115894,
        -1.9973963200158908
      ]
    ]
  },
  "predictions": {
    "onset_ka_over_kappa": 0.18257418583505539,
    "saturated_radius_rad": 0.45643546458763834,
    "single_cell_frequency_Hz": 3.4869100987952835,
    "single_cell_mechanical_power_W": 0.039999999999999994,
    "loaded_radius": 0.2857142857142857,
    "loaded_omega": 0.5477225575051661
  },
  "work_loop": {
    "radius_rad": 0.1,
    "ka_Nm_per_rad": 0.012480000000000002,
    "odd_J": 0.0007841415263360126,
    "reverse_J": -0.0007841415263360126,
    "reciprocal_J": -1.3552527156068805e-20
  },
  "checks": {
    "RK45_DOP853_radius_difference": 1.4215295607300504e-11,
    "perturbed_radius": 0.456435464588217
  },
  "connectivity_2026": {
    "c1": 0.421875,
    "c2": 0.703125,
    "peak_ka_over_kappa": 1.539600717839002,
    "peak_scaled_odd_modulus": 1.1547005383792515,
    "scope": "periodic diluted geometry of Eq.1, not a universal law"
  },
  "encoder_reanalysis": [
    {
      "condition": "zero",
      "epsilon_recorded": 0.0,
      "samples": 839,
      "duration_s": 16.76,
      "fit_samples": 800,
      "omega_shape_rad_per_s": -0.0002794306835620345,
      "inferred_velocity_m_per_s": -2.0012748543200257e-05,
      "mean_shear_amplitude": 0.41439542871100654
    },
    {
      "condition": "small",
      "epsilon_recorded": 0.002,
      "samples": 562,
      "duration_s": 11.22,
      "fit_samples": 562,
      "omega_shape_rad_per_s": -0.0006959585015907382,
      "inferred_velocity_m_per_s": -4.984435607174762e-05,
      "mean_shear_amplitude": 0.41443652471084336
    },
    {
      "condition": "medium",
      "epsilon_recorded": 0.007,
      "samples": 2408,
      "duration_s": 48.14,
      "fit_samples": 800,
      "omega_shape_rad_per_s": 6.409096982900102,
      "inferred_velocity_m_per_s": 0.4590177595127567,
      "mean_shear_amplitude": 0.44865473040543835
    },
    {
      "condition": "positive",
      "epsilon_recorded": 0.01,
      "samples": 3073,
      "duration_s": 61.44,
      "fit_samples": 800,
      "omega_shape_rad_per_s": 9.231891299509908,
      "inferred_velocity_m_per_s": 0.6611855104818284,
      "mean_shear_amplitude": 0.6278755843204198
    },
    {
      "condition": "negative",
      "epsilon_recorded": -0.01,
      "samples": 1363,
      "duration_s": 27.24,
      "fit_samples": 800,
      "omega_shape_rad_per_s": -8.392214012119915,
      "inferred_velocity_m_per_s": -0.6010480545812783,
      "mean_shear_amplitude": 0.7604588048939601
    }
  ],
  "data_limits": [
    "Five selected runs, not all trials. Last 800 samples follow author fit window.",
    "Speed inferred under negligible slip and two shear cycles per rotation; not independent COM tracking.",
    "Defect table normalized to its zero-defect value; no uncertain absolute calibration or synthetic appended rows used."
  ]
}