{
  "predictions": {
    "correction_ratio_z_over_exp_minus_1": {
      "z": [
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        0.03,
        0.1,
        0.3,
        1.0,
        3.0,
        10.0
      ],
      "observed": [
        0.9950083333194444,
        0.9850749988750241,
        0.950833194477505,
        0.8574887740530248,
        0.5819767068693265,
        0.15718708947376786,
        0.00045401991009687764
      ],
      "small_z_relative_error": 8.375195421494339e-06,
      "large_z_ratio_to_zexp_minus_z": 1.0000454019910094,
      "predicted_limits": "1 as z->0; 1 as z->infinity after dividing by z exp(-z)"
    },
    "curvature_bound": {
      "predicted": "all finite-difference margins >= 0",
      "observed": [
        {
          "t": 0.005,
          "min_margin": 1.0,
          "violations": 0,
          "points": 15
        },
        {
          "t": 0.02,
          "min_margin": 1.0053770331805794,
          "violations": 0,
          "points": 15
        },
        {
          "t": 0.08,
          "min_margin": 1.970915130161302,
          "violations": 0,
          "points": 15
        },
        {
          "t": 0.2,
          "min_margin": 1.2016324472366842,
          "violations": 0,
          "points": 15
        }
      ]
    },
    "boundary_leakage": {
      "predicted": "killed 0; Gaussian increases with t",
      "observed": [
        {
          "t": 0.005,
          "gaussian_negative_rate": 0.2068,
          "killed_negative_rate": 0.0
        },
        {
          "t": 0.02,
          "gaussian_negative_rate": 0.2643,
          "killed_negative_rate": 0.0
        },
        {
          "t": 0.08,
          "gaussian_negative_rate": 0.3033,
          "killed_negative_rate": 0.0
        },
        {
          "t": 0.2,
          "gaussian_negative_rate": 0.32895,
          "killed_negative_rate": 0.0
        }
      ]
    }
  },
  "model_comparison": {
    "baseline_gaussian_clip": {
      "mse": 5.473271098669968,
      "near_boundary_mse": 104.1750073306232,
      "device": "cuda"
    },
    "killed_kernel": {
      "mse": 35.25710593069508,
      "near_boundary_mse": 2507.843515863984,
      "device": "cuda"
    }
  }
}