1{
  2  "device": "cuda",
  3  "seed": 1445,
  4  "math_check": {
  5    "max_radial_identity_error": 6.938893903907228e-16,
  6    "speed_decay_sweep": [
  7      {
  8        "kv": 0.5,
  9        "predicted_rate": 0.5,
 10        "observed_rate": 0.5,
 11        "max_identity_error": 1.1102230246251565e-16
 12      },
 13      {
 14        "kv": 1.0,
 15        "predicted_rate": 1.0,
 16        "observed_rate": 1.0,
 17        "max_identity_error": 2.220446049250313e-16
 18      },
 19      {
 20        "kv": 2.0,
 21        "predicted_rate": 2.0,
 22        "observed_rate": 2.0,
 23        "max_identity_error": 0.0
 24      },
 25      {
 26        "kv": 3.0,
 27        "predicted_rate": 3.0,
 28        "observed_rate": 3.0,
 29        "max_identity_error": 2.220446049250313e-16
 30      }
 31    ],
 32    "steering_decay_sweep": [
 33      {
 34        "v": 0.01,
 35        "predicted_rate": 0.19999999999999998,
 36        "observed_rate": 0.20000000000000043,
 37        "relative_error": 2.220446049250313e-15
 38      },
 39      {
 40        "v": 0.05,
 41        "predicted_rate": 0.6,
 42        "observed_rate": 0.5999999999999995,
 43        "relative_error": 7.401486830834377e-16
 44      },
 45      {
 46        "v": 0.1,
 47        "predicted_rate": 0.7999999999999998,
 48        "observed_rate": 0.8000000000000008,
 49        "relative_error": 1.2490009027033013e-15
 50      },
 51      {
 52        "v": 0.2,
 53        "predicted_rate": 0.96,
 54        "observed_rate": 0.9600000000000009,
 55        "relative_error": 9.251858538542972e-16
 56      },
 57      {
 58        "v": 0.5,
 59        "predicted_rate": 1.0909090909090908,
 60        "observed_rate": 1.0909090909090902,
 61        "relative_error": 6.106226635438361e-16
 62      },
 63      {
 64        "v": 1.0,
 65        "predicted_rate": 1.1428571428571428,
 66        "observed_rate": 1.1428571428571421,
 67        "relative_error": 5.828670879282072e-16
 68      },
 69      {
 70        "v": 2.0,
 71        "predicted_rate": 1.1707317073170733,
 72        "observed_rate": 1.1707317073170733,
 73        "relative_error": 0.0
 74      }
 75    ],
 76    "epsilon_transition_sweep": [
 77      {
 78        "r": 0.01,
 79        "predicted_abs_geometric_residual": 30.683234470668992,
 80        "observed_abs_gamma_residual": 30.68323447066898,
 81        "relative_error": 3.4736041425456412e-16
 82      },
 83      {
 84        "r": 0.025,
 85        "predicted_abs_geometric_residual": 7.670808617667248,
 86        "observed_abs_gamma_residual": 7.670808617667237,
 87        "relative_error": 1.3894416570182565e-15
 88      },
 89      {
 90        "r": 0.04,
 91        "predicted_abs_geometric_residual": 1.917702154416812,
 92        "observed_abs_gamma_residual": 1.9177021544168014,
 93        "relative_error": 5.557766628073026e-15
 94      },
 95      {
 96        "r": 0.05,
 97        "predicted_abs_geometric_residual": 0.0,
 98        "observed_abs_gamma_residual": 1.0547118733938987e-14,
 99        "relative_error": 1.0547118733938987e-06
100      },
101      {
102        "r": 0.075,
103        "predicted_abs_geometric_residual": 0.0,
104        "observed_abs_gamma_residual": 1.1102230246251565e-16,
105        "relative_error": 1.1102230246251565e-08
106      },
107      {
108        "r": 0.1,
109        "predicted_abs_geometric_residual": 0.0,
110        "observed_abs_gamma_residual": 1.1102230246251565e-16,
111        "relative_error": 1.1102230246251565e-08
112      },
113      {
114        "r": 0.2,
115        "predicted_abs_geometric_residual": 0.0,
116        "observed_abs_gamma_residual": 9.992007221626409e-16,
117        "relative_error": 9.992007221626409e-08
118      },
119      {
120        "r": 0.5,
121        "predicted_abs_geometric_residual": 0.0,
122        "observed_abs_gamma_residual": 1.1102230246251565e-16,
123        "relative_error": 1.1102230246251565e-08
124      },
125      {
126        "r": 1.0,
127        "predicted_abs_geometric_residual": 0.0,
128        "observed_abs_gamma_residual": 1.1102230246251565e-16,
129        "relative_error": 1.1102230246251565e-08
130      }
131    ]
132  },
133  "policy_comparison": {
134    "unconstrained_polar_residual": {
135      "task_mse": 0.0007122126407921314,
136      "positive_drift_fraction": 0.130859375,
137      "mean_drift_plus_lambdaV": -0.1348373144865036,
138      "mean_V": 1.8700960874557495
139    },
140    "lyapunov_residual": {
141      "task_mse": 0.06113187596201897,
142      "positive_drift_fraction": 0.10888671875,
143      "mean_drift_plus_lambdaV": -0.20551252365112305,
144      "mean_V": 1.885925531387329
145    }
146  },
147  "interpretation": {
148    "speed_prediction": "e_dot=-kv*e exactly",
149    "steering_prediction": "-gamma_dot/gamma=kg*v/(abs(v)+epsilon) for positive v",
150    "epsilon_prediction": "geometric gamma residual is exactly zero for r>=epsilon and scales as 1/r-1/epsilon below epsilon"
151  }
152}