1{
  2  "seed": 7,
  3  "math_check": {
  4    "P": [
  5      [
  6        1.2500000000000002,
  7        0.25
  8      ],
  9      [
 10        0.25000000000000006,
 11        0.37500000000000006
 12      ]
 13    ],
 14    "identity_error": 1.1102230246251565e-16,
 15    "gamma": 0.002734749554788495,
 16    "max_backup_u_on_certificate": 0.17404742623406258,
 17    "observed_min_neg_vdot_over_V": 0.7596534626874615,
 18    "predicted_rate_bound": 0.7596526541079154,
 19    "certificate_saturation_free": true
 20  },
 21  "prediction_1_dissipation": "-Vdot/V >= 1/lambda_max(P) on unsaturated certificate",
 22  "prediction_2_horizon": "backward reachable volume is nondecreasing with T",
 23  "prediction_3_scaling": "quadratic certificate area scales as terminal_radius^2",
 24  "certificate_scaling_sweep": [
 25    {
 26      "terminal_radius": 0.03,
 27      "certified_area": 0.0033698514343115014,
 28      "area_over_base": 0.25,
 29      "predicted_ratio": 0.25
 30    },
 31    {
 32      "terminal_radius": 0.06,
 33      "certified_area": 0.013479405737246005,
 34      "area_over_base": 1.0,
 35      "predicted_ratio": 1.0
 36    },
 37    {
 38      "terminal_radius": 0.12,
 39      "certified_area": 0.05391762294898402,
 40      "area_over_base": 4.0,
 41      "predicted_ratio": 4.0
 42    },
 43    {
 44      "terminal_radius": 0.18,
 45      "certified_area": 0.12131465163521406,
 46      "area_over_base": 9.0,
 47      "predicted_ratio": 9.0
 48    }
 49  ],
 50  "reachability_sweep": [
 51    {
 52      "T": 0.5,
 53      "volume": 0.025200000000000007,
 54      "fraction": 0.0018812147272238647
 55    },
 56    {
 57      "T": 1.0,
 58      "volume": 0.08280000000000001,
 59      "fraction": 0.006181134103735555
 60    },
 61    {
 62      "T": 2.0,
 63      "volume": 0.6228000000000001,
 64      "fraction": 0.046492878258532655
 65    },
 66    {
 67      "T": 3.0,
 68      "volume": 3.387600000000001,
 69      "fraction": 0.2528890083310938
 70    },
 71    {
 72      "T": 4.0,
 73      "volume": 8.341200000000002,
 74      "fraction": 0.6226820747110992
 75    }
 76  ],
 77  "input_saturation_sweep": [
 78    {
 79      "kp": 0.5,
 80      "saturated_fraction": 0.7165775401069518
 81    },
 82    {
 83      "kp": 1.0,
 84      "saturated_fraction": 0.7486631016042781
 85    },
 86    {
 87      "kp": 2.0,
 88      "saturated_fraction": 0.6737967914438503
 89    },
 90    {
 91      "kp": 4.0,
 92      "saturated_fraction": 0.9090909090909091
 93    },
 94    {
 95      "kp": 8.0,
 96      "saturated_fraction": 0.9090909090909091
 97    }
 98  ],
 99  "certified_rollout_audit": {
100    "n": 500,
101    "safe_rate": 1.0,
102    "terminal_rate": 1.0,
103    "max_violation": 0.0,
104    "horizon": 4.0
105  },
106  "policy_comparison": {
107    "n": 1000,
108    "baseline_violation_rate": 0.962,
109    "shield_violation_rate": 0.228,
110    "baseline_mean_violation": 14.94174058032316,
111    "shield_mean_violation": 0.08638416745996397,
112    "shield_mean_switches": 628.568
113  }
114}