1{
 2  "seed": 3002,
 3  "n": 20,
 4  "delta": 0.1,
 5  "reps": 200000,
 6  "moment_check": {
 7    "1": {
 8      "empirical": 0.9523219823374796,
 9      "theory": 0.9523809523809523,
10      "abs_error": 5.897004347277246e-05
11    },
12    "2": {
13      "empirical": 0.9089856354477753,
14      "theory": 0.9090909090909091,
15      "abs_error": 0.00010527364313372978
16    },
17    "5": {
18      "empirical": 0.7998104126740451,
19      "theory": 0.8,
20      "abs_error": 0.0001895873259549763
21    },
22    "10": {
23      "empirical": 0.6664358861689239,
24      "theory": 0.6666666666666667,
25      "abs_error": 0.00023078049774283294
26    }
27  },
28  "beta_upper_quantile": 0.10874906186625444,
29  "scalar_beta_coverage": 0.899365,
30  "deletion_checks": {
31    "scalar_max": {
32      "boundary_size": 1.0,
33      "equivalence_rate": 0.9499999999999997,
34      "projectivity_rate": 1.0
35    },
36    "adaptive_rank_control": {
37      "boundary_size": 1.0,
38      "equivalence_rate": 0.9071749999999997,
39      "projectivity_rate": 0.9546605263157896
40    }
41  },
42  "mini_experiment": {
43    "batches": 1000,
44    "test_points_per_batch": 10000,
45    "baseline_split_conformal_coverage": 0.889,
46    "projective_boundary_beta_coverage": 0.889,
47    "unstable_control_false_beta_coverage": 0.404,
48    "mean_scalar_true_risk": 0.047448855636694875,
49    "mean_adaptive_control_risk": 0.22837482515636362
50  },
51  "interpretation": "Max order-statistic has K=1, exact Beta(1,n), and passes deletion tests; adaptive rank is not projective and its naive K-only beta certificate fails."
52}