{
  "seed": 2915,
  "model": "scalar stable nonlinear plant with phi_gamma(x)=gamma*tanh(x), P=1, C=1",
  "math": {
    "a": 1.0,
    "observer_gain": 0.5,
    "rho": "gamma",
    "alpha": "gamma^2",
    "certificate_at_eps_gamma": "M=-2*(a+L)+4*gamma",
    "predicted_certificate_boundary_gamma": 0.75,
    "predicted_exact_local_boundary_gamma": 1.5
  },
  "bound_check": {
    "rho_theory": 1.7,
    "rho_sample_max": 1.6856403581609258,
    "alpha_theory": 2.8899999999999997,
    "alpha_sample_max": 2.8413834170608943,
    "bounds_hold": true
  },
  "boundary_sweep": {
    "predicted_certificate_boundary": 0.75,
    "observed_certificate_sign_grid_gamma": 0.8,
    "predicted_exact_local_boundary": 1.5,
    "observed_exact_local_boundary": 1.5,
    "rows": [
      {
        "gamma": 0.0,
        "M": -2.0,
        "contracted": true,
        "final_abs_error": 1.2325345334126954e-05
      },
      {
        "gamma": 0.1,
        "M": -2.5999999999999996,
        "contracted": true,
        "final_abs_error": 2.6669364910275975e-05
      },
      {
        "gamma": 0.2,
        "M": -2.1999999999999997,
        "contracted": true,
        "final_abs_error": 5.753929905961615e-05
      },
      {
        "gamma": 0.30000000000000004,
        "M": -1.7999999999999996,
        "contracted": true,
        "final_abs_error": 0.00012371847081870573
      },
      {
        "gamma": 0.4,
        "M": -1.4,
        "contracted": true,
        "final_abs_error": 0.0002649381376100109
      },
      {
        "gamma": 0.5,
        "M": -1.0,
        "contracted": true,
        "final_abs_error": 0.0005645946025852013
      },
      {
        "gamma": 0.6000000000000001,
        "M": -0.5999999999999996,
        "contracted": true,
        "final_abs_error": 0.0011960280402718135
      },
      {
        "gamma": 0.7000000000000001,
        "M": -0.19999999999999973,
        "contracted": false,
        "final_abs_error": 0.0025149237900349746
      },
      {
        "gamma": 0.8,
        "M": 0.2000000000000003,
        "contracted": false,
        "final_abs_error": 0.005238484502105017
      },
      {
        "gamma": 0.9,
        "M": 0.6000000000000001,
        "contracted": false,
        "final_abs_error": 0.010777303443079332
      },
      {
        "gamma": 1.0,
        "M": 1.0,
        "contracted": false,
        "final_abs_error": 0.02180294320185896
      },
      {
        "gamma": 1.1,
        "M": 1.4000000000000004,
        "contracted": false,
        "final_abs_error": 0.043071333794499796
      },
      {
        "gamma": 1.2000000000000002,
        "M": 1.8000000000000007,
        "contracted": false,
        "final_abs_error": 0.0821543213074896
      },
      {
        "gamma": 1.3,
        "M": 2.2,
        "contracted": false,
        "final_abs_error": 0.14866262209584083
      },
      {
        "gamma": 1.4000000000000001,
        "M": 2.6000000000000005,
        "contracted": false,
        "final_abs_error": 0.24934919525635033
      },
      {
        "gamma": 1.5,
        "M": 3.0,
        "contracted": false,
        "final_abs_error": 0.3799753436001856
      },
      {
        "gamma": 1.6,
        "M": 3.4000000000000004,
        "contracted": false,
        "final_abs_error": 0.5246809863124708
      },
      {
        "gamma": 1.7000000000000002,
        "M": 3.8000000000000007,
        "contracted": false,
        "final_abs_error": 0.6675106189902515
      },
      {
        "gamma": 1.8,
        "M": 4.2,
        "contracted": false,
        "final_abs_error": 0.8007194816329817
      },
      {
        "gamma": 1.9000000000000001,
        "M": 4.6000000000000005,
        "contracted": false,
        "final_abs_error": 0.9231093368791489
      },
      {
        "gamma": 2.0,
        "M": 5.0,
        "contracted": false,
        "final_abs_error": 1.0360447636667052
      },
      {
        "gamma": 2.1,
        "M": 5.4,
        "contracted": false,
        "final_abs_error": 1.1413245655791728
      },
      {
        "gamma": 2.2,
        "M": 5.800000000000001,
        "contracted": false,
        "final_abs_error": 1.2405096610805566
      }
    ]
  },
  "rate_sweep": [
    {
      "gamma": 0.0,
      "certificate_upper_bound_logV_slope": -2.0,
      "observed_logV_slope": -2.9999999999998694,
      "bound_holds": true
    },
    {
      "gamma": 0.2,
      "certificate_upper_bound_logV_slope": -2.1999999999999997,
      "observed_logV_slope": -2.600002133424236,
      "bound_holds": true
    },
    {
      "gamma": 0.5,
      "certificate_upper_bound_logV_slope": -1.0,
      "observed_logV_slope": -2.0000095768029373,
      "bound_holds": true
    },
    {
      "gamma": 0.8,
      "certificate_upper_bound_logV_slope": 0.2000000000000003,
      "observed_logV_slope": -1.400029774007129,
      "bound_holds": true
    },
    {
      "gamma": 1.0,
      "certificate_upper_bound_logV_slope": 1.0,
      "observed_logV_slope": -1.0000611689791186,
      "bound_holds": true
    },
    {
      "gamma": 1.2,
      "certificate_upper_bound_logV_slope": 1.7999999999999998,
      "observed_logV_slope": -0.6001268505573438,
      "bound_holds": true
    },
    {
      "gamma": 1.4,
      "certificate_upper_bound_logV_slope": 2.5999999999999996,
      "observed_logV_slope": -0.20027019585083689,
      "bound_holds": true
    }
  ],
  "gain_sweep": {
    "predicted_min_gain_for_kappa_0.8": 1.7999999999999998,
    "observed_grid_min_gain": 1.8,
    "rows": [
      {
        "gain": 0,
        "certificate_kappa": -2.8,
        "meets_target": false
      },
      {
        "gain": 0.1,
        "certificate_kappa": -2.5999999999999996,
        "meets_target": false
      },
      {
        "gain": 0.2,
        "certificate_kappa": -2.4,
        "meets_target": false
      },
      {
        "gain": 0.3,
        "certificate_kappa": -2.1999999999999997,
        "meets_target": false
      },
      {
        "gain": 0.4,
        "certificate_kappa": -2.0,
        "meets_target": false
      },
      {
        "gain": 0.5,
        "certificate_kappa": -1.7999999999999998,
        "meets_target": false
      },
      {
        "gain": 0.7,
        "certificate_kappa": -1.4,
        "meets_target": false
      },
      {
        "gain": 1.0,
        "certificate_kappa": -0.7999999999999998,
        "meets_target": false
      },
      {
        "gain": 1.5,
        "certificate_kappa": 0.20000000000000018,
        "meets_target": false
      },
      {
        "gain": 1.8,
        "certificate_kappa": 0.7999999999999998,
        "meets_target": true
      },
      {
        "gain": 2.0,
        "certificate_kappa": 1.2000000000000004,
        "meets_target": true
      }
    ]
  },
  "noisy_comparison": {
    "baseline_no_observer": {
      "mean_mse": 0.0012980416654828559,
      "std_mse": 0.0
    },
    "certified_observer": {
      "mean_mse": 2.4163893171045498e-05,
      "std_mse": 1.0999791075781146e-05
    }
  }
}