{
  "description": "Finite categorical verification of KL-budgeted Poisson-race sampling",
  "n_samples_per_case": 30000,
  "vocab": 16,
  "cases": [
    {
      "name": "identical",
      "kl_bits": 0.0,
      "l1": 0.0,
      "upper_bound_bits": 0.0,
      "theorem_lower_bound_bits": 0.0,
      "race_tv": 0.0072999999999999975,
      "rejection_tv": 0.007766666666666668,
      "race_mean_log2_index": 0.0,
      "race_mean_index": 1.0,
      "rejection_mean_index": 1.0,
      "race_p95_index": 1.0,
      "rejection_p95_index": 1.0,
      "race_seconds": 3.3220963799976744,
      "rejection_seconds": 2.487022307002917,
      "race_target_evals_per_sample": 1.0,
      "rejection_target_evals_per_sample": 1.0
    },
    {
      "name": "close",
      "kl_bits": 0.014802870363051963,
      "l1": 0.07499999999999993,
      "upper_bound_bits": 0.12355287036305185,
      "theorem_lower_bound_bits": 0.037499999999999964,
      "race_tv": 0.007900000000000004,
      "rejection_tv": 0.009666666666666664,
      "race_mean_log2_index": 0.48917881130677277,
      "race_mean_index": 1.5992,
      "rejection_mean_index": 1.6043666666666667,
      "race_p95_index": 4.0,
      "rejection_p95_index": 4.0,
      "race_seconds": 4.527122490020702,
      "rejection_seconds": 3.49707968000439,
      "race_target_evals_per_sample": 1.0,
      "rejection_target_evals_per_sample": 1.0
    },
    {
      "name": "moderate",
      "kl_bits": 0.3838856838433442,
      "l1": 0.47500000000000003,
      "upper_bound_bits": 1.0726356838433442,
      "theorem_lower_bound_bits": 0.23750000000000002,
      "race_tv": 0.006599999999999981,
      "rejection_tv": 0.006466666666666669,
      "race_mean_log2_index": 1.7533844770007623,
      "race_mean_index": 4.768266666666666,
      "rejection_mean_index": 4.812566666666667,
      "race_p95_index": 13.0,
      "rejection_p95_index": 13.0,
      "race_seconds": 11.626685801980784,
      "rejection_seconds": 9.96556899198913,
      "race_target_evals_per_sample": 1.0,
      "rejection_target_evals_per_sample": 1.0
    },
    {
      "name": "farther",
      "kl_bits": 1.4662931673019237,
      "l1": 1.0749999999999997,
      "upper_bound_bits": 3.0250431673019236,
      "theorem_lower_bound_bits": 0.7331465836509619,
      "race_tv": 0.010199999999999978,
      "rejection_tv": 0.006233333333333325,
      "race_mean_log2_index": 2.6456972131135568,
      "race_mean_index": 9.6289,
      "rejection_mean_index": 9.6629,
      "race_p95_index": 28.0,
      "rejection_p95_index": 28.0,
      "race_seconds": 22.22676015799516,
      "rejection_seconds": 18.396968259010464,
      "race_target_evals_per_sample": 1.0,
      "rejection_target_evals_per_sample": 1.0
    }
  ],
  "notes": [
    "Race samples use iid P marks and Exp(1) arrivals; stopping uses known max Q/P.",
    "TV is halved L1, while the theorem's displayed L1 is reported separately.",
    "Target evaluation count is not a speed advantage here: q is explicitly available; this is an exactness/candidate-index test."
  ]
}