1{
 2  "description": "Finite categorical verification of KL-budgeted Poisson-race sampling",
 3  "n_samples_per_case": 30000,
 4  "vocab": 16,
 5  "cases": [
 6    {
 7      "name": "identical",
 8      "kl_bits": 0.0,
 9      "l1": 0.0,
10      "upper_bound_bits": 0.0,
11      "theorem_lower_bound_bits": 0.0,
12      "race_tv": 0.0072999999999999975,
13      "rejection_tv": 0.007766666666666668,
14      "race_mean_log2_index": 0.0,
15      "race_mean_index": 1.0,
16      "rejection_mean_index": 1.0,
17      "race_p95_index": 1.0,
18      "rejection_p95_index": 1.0,
19      "race_seconds": 3.3220963799976744,
20      "rejection_seconds": 2.487022307002917,
21      "race_target_evals_per_sample": 1.0,
22      "rejection_target_evals_per_sample": 1.0
23    },
24    {
25      "name": "close",
26      "kl_bits": 0.014802870363051963,
27      "l1": 0.07499999999999993,
28      "upper_bound_bits": 0.12355287036305185,
29      "theorem_lower_bound_bits": 0.037499999999999964,
30      "race_tv": 0.007900000000000004,
31      "rejection_tv": 0.009666666666666664,
32      "race_mean_log2_index": 0.48917881130677277,
33      "race_mean_index": 1.5992,
34      "rejection_mean_index": 1.6043666666666667,
35      "race_p95_index": 4.0,
36      "rejection_p95_index": 4.0,
37      "race_seconds": 4.527122490020702,
38      "rejection_seconds": 3.49707968000439,
39      "race_target_evals_per_sample": 1.0,
40      "rejection_target_evals_per_sample": 1.0
41    },
42    {
43      "name": "moderate",
44      "kl_bits": 0.3838856838433442,
45      "l1": 0.47500000000000003,
46      "upper_bound_bits": 1.0726356838433442,
47      "theorem_lower_bound_bits": 0.23750000000000002,
48      "race_tv": 0.006599999999999981,
49      "rejection_tv": 0.006466666666666669,
50      "race_mean_log2_index": 1.7533844770007623,
51      "race_mean_index": 4.768266666666666,
52      "rejection_mean_index": 4.812566666666667,
53      "race_p95_index": 13.0,
54      "rejection_p95_index": 13.0,
55      "race_seconds": 11.626685801980784,
56      "rejection_seconds": 9.96556899198913,
57      "race_target_evals_per_sample": 1.0,
58      "rejection_target_evals_per_sample": 1.0
59    },
60    {
61      "name": "farther",
62      "kl_bits": 1.4662931673019237,
63      "l1": 1.0749999999999997,
64      "upper_bound_bits": 3.0250431673019236,
65      "theorem_lower_bound_bits": 0.7331465836509619,
66      "race_tv": 0.010199999999999978,
67      "rejection_tv": 0.006233333333333325,
68      "race_mean_log2_index": 2.6456972131135568,
69      "race_mean_index": 9.6289,
70      "rejection_mean_index": 9.6629,
71      "race_p95_index": 28.0,
72      "rejection_p95_index": 28.0,
73      "race_seconds": 22.22676015799516,
74      "rejection_seconds": 18.396968259010464,
75      "race_target_evals_per_sample": 1.0,
76      "rejection_target_evals_per_sample": 1.0
77    }
78  ],
79  "notes": [
80    "Race samples use iid P marks and Exp(1) arrivals; stopping uses known max Q/P.",
81    "TV is halved L1, while the theorem's displayed L1 is reported separately.",
82    "Target evaluation count is not a speed advantage here: q is explicitly available; this is an exactness/candidate-index test."
83  ]
84}