{
  "seed": 2081,
  "system": "xdot=u, h=x, alpha=1",
  "epsilon": 0.08,
  "certificate": {
    "L": 1.0,
    "rows": [
      {
        "n": 3,
        "delta": 0.25,
        "L": 1.0,
        "predicted_lower": -0.16999999999999998,
        "actual_min": -0.07915494309189534,
        "observed_gap": 0.15915494309189535,
        "positive_certificate": false,
        "actual_safe": false
      },
      {
        "n": 5,
        "delta": 0.125,
        "L": 1.0,
        "predicted_lower": -0.045,
        "actual_min": 0.00042252845405232886,
        "observed_gap": 0.07957747154594767,
        "positive_certificate": false,
        "actual_safe": true
      },
      {
        "n": 9,
        "delta": 0.0625,
        "L": 1.0,
        "predicted_lower": 0.0175,
        "actual_min": 0.040211264227026165,
        "observed_gap": 0.039788735772973836,
        "positive_certificate": true,
        "actual_safe": true
      },
      {
        "n": 17,
        "delta": 0.03125,
        "L": 1.0,
        "predicted_lower": 0.04875,
        "actual_min": 0.06010563211351308,
        "observed_gap": 0.01989436788648692,
        "positive_certificate": true,
        "actual_safe": true
      },
      {
        "n": 33,
        "delta": 0.015625,
        "L": 1.0,
        "predicted_lower": 0.064375,
        "actual_min": 0.07005281605675655,
        "observed_gap": 0.009947183943243454,
        "positive_certificate": true,
        "actual_safe": true
      },
      {
        "n": 65,
        "delta": 0.0078125,
        "L": 1.0,
        "predicted_lower": 0.0721875,
        "actual_min": 0.07502640928501522,
        "observed_gap": 0.00497359071498478,
        "positive_certificate": true,
        "actual_safe": true
      },
      {
        "n": 129,
        "delta": 0.00390625,
        "L": 1.0,
        "predicted_lower": 0.07609375,
        "actual_min": 0.07751320464250762,
        "observed_gap": 0.002486795357492383,
        "positive_certificate": true,
        "actual_safe": true
      }
    ],
    "predicted_boundary_delta": 0.08,
    "observed_safe_boundary_delta": 0.125,
    "pairwise_lipschitz_excess": 0.0,
    "prediction_checks": {
      "lower_bound_holds": true,
      "gap_ratio_predicted": 0.6366197723675814,
      "gap_ratio_max_error": 1.6084953136097369e-07,
      "observed_loglog_slope": 1.000000065091794,
      "predicted_slope": 1.0,
      "boundary_prediction_conservative": true,
      "all_checks": true
    },
    "observed_gap_over_delta": [
      0.6366197723675814,
      0.6366197723675814,
      0.6366197723675814,
      0.6366197723675815,
      0.636619772367581,
      0.6366196115180518,
      0.63661961151805
    ]
  },
  "training": {
    "baseline_task_only": {
      "final_x": -0.4481355547904968,
      "min_x": -0.4481355547904968,
      "min_r": -0.6048622727394104,
      "task_terminal_error": 0.0018644332885742188,
      "barrier_violation_fraction": 1.0,
      "dense_unseen_min_r": -0.44501107931137085
    },
    "barrier_certified": {
      "final_x": 0.09715487062931061,
      "min_x": 0.09715487062931061,
      "min_r": 0.08067892491817474,
      "task_terminal_error": 0.5471548438072205,
      "barrier_violation_fraction": 0.0,
      "dense_unseen_min_r": 0.0788109228014946
    }
  }
}