outputs/claim2.json

{
  "assessment": "verified",
  "constant_boundary_ks_improves_1e4_to_1e8": true,
  "paper_native_paths_per_cell": 5000,
  "stopping_time_clt": [
    {
      "boundary": "theoretical",
      "distribution": "Bernoulli(0.6)",
      "log10_alpha": -4,
      "m0": 0.2,
      "maximum_simulated_step": 102,
      "mean_tau": 37.4672,
      "normal_ks": 0.4009024336465053,
      "oracle": {
        "ell_x0": -0.693147180559945,
        "ell_x1": 1.0986122886681096,
        "kl_inf": 0.3819085009768876,
        "lambda_star": -2.499999999999999,
        "m0": 0.2,
        "p": 0.6,
        "sigma_squared": 0.7704964789364159,
        "stopping_sigma_squared": 13.832245291385126
      },
      "paths": 5000,
      "single_path_plugin_ci_empirical_coverage": 0.8286,
      "standardized_mean": 1.182813050633105,
      "standardized_variance": 1.827688349949487,
      "tau_quantiles_025_50_975": [
        12.0,
        37.0,
        72.0
      ]
    },
    {
      "boundary": "theoretical",
      "distribution": "Bernoulli(0.6)",
      "log10_alpha": -8,
      "m0": 0.2,
      "maximum_simulated_step": 153,
      "mean_tau": 63.4144,
      "normal_ks": 0.33497018553985086,
      "oracle": {
        "ell_x0": -0.693147180559945,
        "ell_x1": 1.0986122886681096,
        "kl_inf": 0.3819085009768876,
        "lambda_star": -2.499999999999999,
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        "sigma_squared": 0.7704964789364159,
        "stopping_sigma_squared": 13.832245291385126
      },
      "paths": 5000,
      "single_path_plugin_ci_empirical_coverage": 0.885,
      "standardized_mean": 0.9510559162163594,
      "standardized_variance": 1.444734601034845,
      "tau_quantiles_025_50_975": [
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        62.0,
        105.0
      ]
    },
    {
      "boundary": "constant",
      "distribution": "Bernoulli(0.6)",
      "log10_alpha": -4,
      "m0": 0.2,
      "maximum_simulated_step": 77,
      "mean_tau": 24.1716,
      "normal_ks": 0.08633869419826778,
      "oracle": {
        "ell_x0": -0.693147180559945,
        "ell_x1": 1.0986122886681096,
        "kl_inf": 0.3819085009768876,
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        "sigma_squared": 0.7704964789364159,
        "stopping_sigma_squared": 13.832245291385126
      },
      "paths": 5000,
      "single_path_plugin_ci_empirical_coverage": 0.8044,
      "standardized_mean": 0.004871449606083055,
      "standardized_variance": 0.9947917156102605,
      "tau_quantiles_025_50_975": [
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        24.0,
        51.0
      ]
    },
    {
      "boundary": "constant",
      "distribution": "Bernoulli(0.6)",
      "log10_alpha": -8,
      "m0": 0.2,
      "maximum_simulated_step": 133,
      "mean_tau": 48.608,
      "normal_ks": 0.05782882090768432,
      "oracle": {
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        "ell_x1": 1.0986122886681096,
        "kl_inf": 0.3819085009768876,
        "lambda_star": -2.499999999999999,
        "m0": 0.2,
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        "sigma_squared": 0.7704964789364159,
        "stopping_sigma_squared": 13.832245291385126
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      "paths": 5000,
      "single_path_plugin_ci_empirical_coverage": 0.8758,
      "standardized_mean": 0.023478216428855638,
      "standardized_variance": 1.021829572881041,
      "tau_quantiles_025_50_975": [
        22.0,
        47.0,
        84.0
      ]
    }
  ],
  "theoretical_boundary_is_more_finite_sample_distorted": true
}