{
  "prediction_1_saturation_and_bound": {
    "equilibrium": {
      "rho_mean": 1.0,
      "rho_max": 1.0000000000000002,
      "rho_fd_max": 1.00000008615521,
      "inequality_max_excess": 2.220446049250313e-16,
      "mean_V": 0.3360484351275103,
      "mean_I": 0.3360484351275103
    },
    "nonequilibrium": {
      "rho_mean": 0.6392402261714853,
      "rho_max": 0.9328673209128918,
      "rho_fd_max": 0.9328674027357408,
      "inequality_max_excess": 0.0,
      "mean_V": 0.34900045177190664,
      "mean_I": 0.46593960068130363
    }
  },
  "prediction_2_delta_scaling_equilibrium": {
    "rows": [
      [
        0.002,
        0.01301229933191362,
        0.0019901795830065128,
        0.00199999999995767,
        0.9950897915032564,
        0.9950897915243173
      ],
      [
        0.004,
        0.02602459866382724,
        0.003961019883030992,
        0.00399999999991534,
        0.9902549707577479,
        0.9902549707787066
      ],
      [
        0.008,
        0.05204919732765448,
        0.007846421958454863,
        0.00799999999983068,
        0.9808027448068579,
        0.9808027448276165
      ],
      [
        0.016,
        0.10409839465530896,
        0.015403380461052385,
        0.01599999999966136,
        0.962711278815774,
        0.9627112788361497
      ],
      [
        0.032,
        0.2081967893106179,
        0.029740352370462797,
        0.03199999999932272,
        0.9293860115769624,
        0.9293860115966328
      ]
    ],
    "step_loglog_slope": 1.0000000000000009,
    "max_actual_over_delta": 0.9950897915032564,
    "max_actual_over_predicted": 0.9950897915243173
  },
  "prediction_2_delta_scaling_nonequilibrium": {
    "rows": [
      [
        0.002,
        0.00811506040080781,
        0.001149412240541603,
        0.0019999999999835366,
        0.5747061202708015,
        0.5747061202755323
      ],
      [
        0.004,
        0.01623012080161562,
        0.002291441738553779,
        0.003999999999967073,
        0.5728604346384447,
        0.5728604346431603
      ],
      [
        0.008,
        0.03246024160323124,
        0.004553728290754899,
        0.007999999999934147,
        0.5692160363443624,
        0.569216036349048
      ],
      [
        0.016,
        0.06492048320646247,
        0.008993708427134428,
        0.015999999999868293,
        0.5621067766959017,
        0.5621067767005289
      ],
      [
        0.032,
        0.12984096641292495,
        0.017553463504265676,
        0.031999999999736586,
        0.5485457345083024,
        0.5485457345128179
      ]
    ],
    "step_loglog_slope": 1.0000000000000007,
    "max_actual_over_delta": 0.5747061202708015,
    "max_actual_over_predicted": 0.5747061202755323
  },
  "prediction_3_schedule_jump_control": {
    "0.01": {
      "cr_updates_to_endpoint": 40,
      "cr_final_beta": 0.4161577319825337,
      "cr_max_jump": 0.00989931754890594,
      "geometric_max_jump": 0.232050840928806,
      "cr_mean_jump": 0.009851687169634743,
      "geometric_mean_jump": 0.023654674272653796,
      "cr_path_first_last": [
        0.2,
        0.4161577319825337
      ]
    },
    "0.03": {
      "cr_updates_to_endpoint": 35,
      "cr_final_beta": 4.0,
      "cr_max_jump": 0.029108193178353226,
      "geometric_max_jump": 0.232050840928806,
      "cr_mean_jump": 0.027033913454461482,
      "geometric_mean_jump": 0.023654674272653796,
      "cr_path_first_last": [
        0.2,
        4.0
      ]
    },
    "0.06": {
      "cr_updates_to_endpoint": 21,
      "cr_final_beta": 4.0,
      "cr_max_jump": 0.05651623307968756,
      "geometric_max_jump": 0.232050840928806,
      "cr_mean_jump": 0.04505652242410246,
      "geometric_mean_jump": 0.023654674272653796,
      "cr_path_first_last": [
        0.2,
        4.0
      ]
    }
  },
  "interpretation": {
    "equilibrium_prediction": "rho=1 exactly because score is -(E-mu) and I=Var(E)",
    "nonequilibrium_prediction": "rho<1 when the beta score contains an F component not determined by E",
    "controller_prediction": "actual energy jump is approximately <= delta for small delta and controller steps scale linearly with delta"
  }
}