{
  "seed": 3002,
  "n": 20,
  "delta": 0.1,
  "reps": 200000,
  "moment_check": {
    "1": {
      "empirical": 0.9523219823374796,
      "theory": 0.9523809523809523,
      "abs_error": 5.897004347277246e-05
    },
    "2": {
      "empirical": 0.9089856354477753,
      "theory": 0.9090909090909091,
      "abs_error": 0.00010527364313372978
    },
    "5": {
      "empirical": 0.7998104126740451,
      "theory": 0.8,
      "abs_error": 0.0001895873259549763
    },
    "10": {
      "empirical": 0.6664358861689239,
      "theory": 0.6666666666666667,
      "abs_error": 0.00023078049774283294
    }
  },
  "beta_upper_quantile": 0.10874906186625444,
  "scalar_beta_coverage": 0.899365,
  "deletion_checks": {
    "scalar_max": {
      "boundary_size": 1.0,
      "equivalence_rate": 0.9499999999999997,
      "projectivity_rate": 1.0
    },
    "adaptive_rank_control": {
      "boundary_size": 1.0,
      "equivalence_rate": 0.9071749999999997,
      "projectivity_rate": 0.9546605263157896
    }
  },
  "mini_experiment": {
    "batches": 1000,
    "test_points_per_batch": 10000,
    "baseline_split_conformal_coverage": 0.889,
    "projective_boundary_beta_coverage": 0.889,
    "unstable_control_false_beta_coverage": 0.404,
    "mean_scalar_true_risk": 0.047448855636694875,
    "mean_adaptive_control_risk": 0.22837482515636362
  },
  "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."
}