{ "alpha": 0.05, "artifact": "serving_limits/formal/leaky_rate_measured.py", "avg_vs_worst_gap": { "adversarial_never_below_uniform": true, "eps_flip_cells": 3, "eps_flip_detail": [ { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.9515, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": false, "uniform_mean_leak_rate": 0.0485 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.9505, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": false, "uniform_mean_leak_rate": 0.0495 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.954375, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": false, "uniform_mean_leak_rate": 0.045625 } ], "max_gap": 0.954375, "note": "How far a reported average eps understates the worst case. ASYMMETRIC BY CONSTRUCTION, and the two arms must NOT be read as two measurements: the adversarial arm is a CONSTRUCTIVE REALIZATION of the theorem's witness (we draw the live set FROM the largest fiber, so a rate of exactly 1.0 is what the construction forces, not an empirical discovery -- its only content is that the witness is realizable in the mirror). The UNIFORM arm is the genuine random quantity, APPROXIMATE with a Clopper-Pearson interval. The gap is therefore (constructed worst case) minus (measured average), not (measured) - (measured).", "pairs": [ { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.8215, "n": 4, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.1785 }, { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.822, "n": 4, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.178 }, { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.63575, "n": 8, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.36425 }, { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.629688, "n": 8, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.370312 }, { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.9515, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": false, "uniform_mean_leak_rate": 0.0485 }, { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.944, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.056 }, { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.89825, "n": 8, "premise_holds": false, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.10175 }, { "N": 256, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.893437, "n": 8, "premise_holds": false, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.106563 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.8205, "n": 4, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.1795 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.828, "n": 4, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.172 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.642125, "n": 8, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.357875 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.633562, "n": 8, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.366438 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.9505, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": false, "uniform_mean_leak_rate": 0.0495 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.954, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.046 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.895625, "n": 8, "premise_holds": true, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.104375 }, { "N": 1024, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.893437, "n": 8, "premise_holds": true, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.106563 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.823875, "n": 4, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.176125 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.819625, "n": 4, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.180375 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.62625, "n": 8, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.37375 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.64375, "n": 8, "premise_holds": true, "s": 16, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.35625 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.954375, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": false, "uniform_mean_leak_rate": 0.045625 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.950375, "n": 4, "premise_holds": true, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.049625 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/10", "gap": 0.893562, "n": 8, "premise_holds": true, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.106438 }, { "N": 4096, "adversarial_exceeds_eps": true, "adversarial_mean_leak_rate": 1.0, "eps": "1/100", "gap": 0.8955, "n": 8, "premise_holds": true, "s": 64, "uniform_exceeds_eps": true, "uniform_mean_leak_rate": 0.1045 } ] }, "balanced_control": { "all_attain_ceil_N_over_s": true, "note": "even the perfectly-balanced isolator has maxFib = ceil(N/s) exactly -- the floor is attained, not merely bounded", "rows": [ { "N": 256, "attains_floor": true, "ceil_N_over_s": 16, "max_fib": 16, "s": 16 }, { "N": 256, "attains_floor": true, "ceil_N_over_s": 4, "max_fib": 4, "s": 64 }, { "N": 1024, "attains_floor": true, "ceil_N_over_s": 64, "max_fib": 64, "s": 16 }, { "N": 1024, "attains_floor": true, "ceil_N_over_s": 16, "max_fib": 16, "s": 64 }, { "N": 4096, "attains_floor": true, "ceil_N_over_s": 256, "max_fib": 256, "s": 16 }, { "N": 4096, "attains_floor": true, "ceil_N_over_s": 64, "max_fib": 64, "s": 64 } ] }, "cells": [ { "N": 256, "any_collision_count": 671, "any_collision_rate": 0.3355, "cp_hi": 0.356673, "cp_lo": 0.314811, "eps": "1/100", "idx": 0, "max_fib": 22, "mean_exceeds_eps": true, "mean_leak_rate": 0.178, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260718, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 1, "max_fib": 22, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260719, "trials": 2000 }, { "N": 256, "any_collision_count": 672, "any_collision_rate": 0.336, "cp_hi": 0.35718, "cp_lo": 0.315302, "eps": "1/10", "idx": 2, "max_fib": 25, "mean_exceeds_eps": true, "mean_leak_rate": 0.1785, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260720, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 3, "max_fib": 23, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260721, "trials": 2000 }, { "N": 256, "any_collision_count": 1780, "any_collision_rate": 0.89, "cp_hi": 0.903384, "cp_lo": 0.875462, "eps": "1/100", "idx": 4, "max_fib": 24, "mean_exceeds_eps": true, "mean_leak_rate": 0.370312, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260722, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 5, "max_fib": 25, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260723, "trials": 2000 }, { "N": 256, "any_collision_count": 1767, "any_collision_rate": 0.8835, "cp_hi": 0.897241, "cp_lo": 0.868624, "eps": "1/10", "idx": 6, "max_fib": 23, "mean_exceeds_eps": true, "mean_leak_rate": 0.36425, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260724, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 7, "max_fib": 22, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260725, "trials": 2000 }, { "N": 256, "any_collision_count": 223, "any_collision_rate": 0.1115, "cp_hi": 0.126118, "cp_lo": 0.098033, "eps": "1/100", "idx": 8, "max_fib": 11, "mean_exceeds_eps": true, "mean_leak_rate": 0.056, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260726, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 9, "max_fib": 10, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260727, "trials": 2000 }, { "N": 256, "any_collision_count": 192, "any_collision_rate": 0.096, "cp_hi": 0.10976, "cp_lo": 0.083439, "eps": "1/10", "idx": 10, "max_fib": 8, "mean_exceeds_eps": false, "mean_leak_rate": 0.0485, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260728, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 11, "max_fib": 10, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260729, "trials": 2000 }, { "N": 256, "any_collision_count": 744, "any_collision_rate": 0.372, "cp_hi": 0.393608, "cp_lo": 0.350768, "eps": "1/100", "idx": 12, "max_fib": 9, "mean_exceeds_eps": true, "mean_leak_rate": 0.106563, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": false, "query_model": "uniform", "s": 64, "seed": 20260730, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 13, "max_fib": 10, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": false, "query_model": "adversarial_cluster", "s": 64, "seed": 20260731, "trials": 2000 }, { "N": 256, "any_collision_count": 717, "any_collision_rate": 0.3585, "cp_hi": 0.379963, "cp_lo": 0.337453, "eps": "1/10", "idx": 14, "max_fib": 11, "mean_exceeds_eps": true, "mean_leak_rate": 0.10175, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": false, "query_model": "uniform", "s": 64, "seed": 20260732, "trials": 2000 }, { "N": 256, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 15, "max_fib": 9, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": false, "query_model": "adversarial_cluster", "s": 64, "seed": 20260733, "trials": 2000 }, { "N": 1024, "any_collision_count": 653, "any_collision_rate": 0.3265, "cp_hi": 0.347545, "cp_lo": 0.305965, "eps": "1/100", "idx": 16, "max_fib": 77, "mean_exceeds_eps": true, "mean_leak_rate": 0.172, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260734, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 17, "max_fib": 72, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260735, "trials": 2000 }, { "N": 1024, "any_collision_count": 681, "any_collision_rate": 0.3405, "cp_hi": 0.36174, "cp_lo": 0.319728, "eps": "1/10", "idx": 18, "max_fib": 83, "mean_exceeds_eps": true, "mean_leak_rate": 0.1795, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260736, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 19, "max_fib": 78, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260737, "trials": 2000 }, { "N": 1024, "any_collision_count": 1762, "any_collision_rate": 0.881, "cp_hi": 0.894874, "cp_lo": 0.865998, "eps": "1/100", "idx": 20, "max_fib": 74, "mean_exceeds_eps": true, "mean_leak_rate": 0.366438, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260738, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 21, "max_fib": 82, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260739, "trials": 2000 }, { "N": 1024, "any_collision_count": 1743, "any_collision_rate": 0.8715, "cp_hi": 0.885864, "cp_lo": 0.856038, "eps": "1/10", "idx": 22, "max_fib": 77, "mean_exceeds_eps": true, "mean_leak_rate": 0.357875, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260740, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 23, "max_fib": 90, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260741, "trials": 2000 }, { "N": 1024, "any_collision_count": 181, "any_collision_rate": 0.0905, "cp_hi": 0.103932, "cp_lo": 0.078284, "eps": "1/100", "idx": 24, "max_fib": 25, "mean_exceeds_eps": true, "mean_leak_rate": 0.046, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260742, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 25, "max_fib": 26, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260743, "trials": 2000 }, { "N": 1024, "any_collision_count": 195, "any_collision_rate": 0.0975, "cp_hi": 0.111347, "cp_lo": 0.084847, "eps": "1/10", "idx": 26, "max_fib": 25, "mean_exceeds_eps": false, "mean_leak_rate": 0.0495, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260744, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 27, "max_fib": 27, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260745, "trials": 2000 }, { "N": 1024, "any_collision_count": 746, "any_collision_rate": 0.373, "cp_hi": 0.394618, "cp_lo": 0.351755, "eps": "1/100", "idx": 28, "max_fib": 25, "mean_exceeds_eps": true, "mean_leak_rate": 0.106563, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260746, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 29, "max_fib": 27, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260747, "trials": 2000 }, { "N": 1024, "any_collision_count": 720, "any_collision_rate": 0.36, "cp_hi": 0.38148, "cp_lo": 0.338932, "eps": "1/10", "idx": 30, "max_fib": 30, "mean_exceeds_eps": true, "mean_leak_rate": 0.104375, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260748, "trials": 2000 }, { "N": 1024, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 31, "max_fib": 26, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260749, "trials": 2000 }, { "N": 4096, "any_collision_count": 681, "any_collision_rate": 0.3405, "cp_hi": 0.36174, "cp_lo": 0.319728, "eps": "1/100", "idx": 32, "max_fib": 279, "mean_exceeds_eps": true, "mean_leak_rate": 0.180375, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260750, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 33, "max_fib": 280, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260751, "trials": 2000 }, { "N": 4096, "any_collision_count": 666, "any_collision_rate": 0.333, "cp_hi": 0.354138, "cp_lo": 0.312353, "eps": "1/10", "idx": 34, "max_fib": 284, "mean_exceeds_eps": true, "mean_leak_rate": 0.176125, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260752, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 35, "max_fib": 271, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260753, "trials": 2000 }, { "N": 4096, "any_collision_count": 1753, "any_collision_rate": 0.8765, "cp_hi": 0.890609, "cp_lo": 0.861277, "eps": "1/100", "idx": 36, "max_fib": 285, "mean_exceeds_eps": true, "mean_leak_rate": 0.35625, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260754, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 37, "max_fib": 273, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260755, "trials": 2000 }, { "N": 4096, "any_collision_count": 1774, "any_collision_rate": 0.887, "cp_hi": 0.90055, "cp_lo": 0.872304, "eps": "1/10", "idx": 38, "max_fib": 290, "mean_exceeds_eps": true, "mean_leak_rate": 0.37375, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 16, "seed": 20260756, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 39, "max_fib": 290, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 16, "seed": 20260757, "trials": 2000 }, { "N": 4096, "any_collision_count": 195, "any_collision_rate": 0.0975, "cp_hi": 0.111347, "cp_lo": 0.084847, "eps": "1/100", "idx": 40, "max_fib": 83, "mean_exceeds_eps": true, "mean_leak_rate": 0.049625, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260758, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 41, "max_fib": 85, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260759, "trials": 2000 }, { "N": 4096, "any_collision_count": 182, "any_collision_rate": 0.091, "cp_hi": 0.104462, "cp_lo": 0.078752, "eps": "1/10", "idx": 42, "max_fib": 83, "mean_exceeds_eps": false, "mean_leak_rate": 0.045625, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260760, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 43, "max_fib": 82, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 4, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260761, "trials": 2000 }, { "N": 4096, "any_collision_count": 731, "any_collision_rate": 0.3655, "cp_hi": 0.38704, "cp_lo": 0.344355, "eps": "1/100", "idx": 44, "max_fib": 81, "mean_exceeds_eps": true, "mean_leak_rate": 0.1045, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260762, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/100", "idx": 45, "max_fib": 82, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260763, "trials": 2000 }, { "N": 4096, "any_collision_count": 746, "any_collision_rate": 0.373, "cp_hi": 0.394618, "cp_lo": 0.351755, "eps": "1/10", "idx": 46, "max_fib": 83, "mean_exceeds_eps": true, "mean_leak_rate": 0.106438, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "uniform", "s": 64, "seed": 20260764, "trials": 2000 }, { "N": 4096, "any_collision_count": 2000, "any_collision_rate": 1.0, "cp_hi": 1.0, "cp_lo": 0.998157, "eps": "1/10", "idx": 47, "max_fib": 84, "mean_exceeds_eps": true, "mean_leak_rate": 1.0, "mirror_violation": false, "n": 8, "premise_s_times_n_minus_1_lt_N": true, "query_model": "adversarial_cluster", "s": 64, "seed": 20260765, "trials": 2000 } ], "gap_table": [ { "assumption": "the active set is chosen ADVERSARIALLY (the adversary picks which n configs are live). If the live set is benign and statistically independent of f, the theorem says NOTHING about the realized leak rate -- that average-case regime is what the uniform arm of this grid measures, and it is covered by NO theorem here", "source": "LeakyRateBound.lean HONEST SCOPE disclosure (1)" }, { "assumption": "f is a TOTAL DETERMINISTIC function. A RANDOMIZED isolator (hash family with a secret per-deployment seed) is OUT OF MODEL; the deterministic-vs-randomized dichotomy is the residual frontier and remains OPEN", "source": "LeakyRateBound.lean HONEST SCOPE disclosure (2)" }, { "assumption": "NOT new mathematics -- a pigeonhole corollary. Prior art: birthday paradox; Bloom (1970) false-positive analysis; Broder-Mitzenmacher AMQ survey; Carter-Wegman universal hashing; differential-privacy rate accounting", "source": "LeakyRateBound.lean HONEST SCOPE disclosure (3)" }, { "assumption": "bound conformance in this grid is a MIRROR TRANSCRIPTION CHECK, not independent evidence for the theorem; the theorem's evidence is the Lean proof + axiom audit", "source": "this file's docstring, measurement (1)" }, { "assumption": "the leak-rate numbers are a SEEDED CPU SIMULATION in the stated model, APPROXIMATE with a Clopper-Pearson interval -- never 'exact'; a FLOOR, no speedup", "source": "repo rule (run_acceptance_sf.py: 'labeled APPROXIMATE, never exact')" }, { "assumption": "the adversarial_cluster arm reports exactly 1.0 in EVERY cell because it draws the live set FROM the largest fiber -- that is TRUE BY CONSTRUCTION, not an empirical result. Only the uniform arm is a genuine random quantity. Do not quote the adversarial arm as a measurement", "source": "avg_vs_worst_gap.note" }, { "assumption": "4 of 48 cells (N=256, s=64, n=8) have premise_holds=false yet still satisfy n <= maxFib -- the premise s*(n-1) < N is SUFFICIENT, not NECESSARY. Those cells are kept and reported, not dropped", "source": "cells[12..15]; mirror_check.cells_premise_holds = 44 of 48" } ], "grid": { "N": [ 256, 1024, 4096 ], "cells_total": 48, "eps": [ "1/100", "1/10" ], "n_active": [ 4, 8 ], "query_models": [ "uniform", "adversarial_cluster" ], "s": [ 16, 64 ] }, "honest_scope": "The WORST-CASE statement is PROVED in Lean (LeakyRateBound.lean, axioms subset of {propext, Quot.sound}); this script does NOT prove it. Measurement (1) is a mirror transcription check. Measurement (2) -- the average-vs-worst leak gap -- is a SEEDED CPU SIMULATION in the stated model, APPROXIMATE with Clopper-Pearson intervals, never 'exact'. The adversarial active set and the deterministic-isolator restriction are DISCLOSED assumptions (gap_table), not results; randomized isolators remain OUT of model and the \u03b5-frontier LeakyIsolationBound documents is NARROWED, not closed. A FLOOR. NO speedup.", "lean_source": "serving_limits/formal/lean/LeakyRateBound.lean", "lean_theorems": [ "LeakyRateBound.max_fiber_floor", "LeakyRateBound.big_fiber_of_small_state", "LeakyRateBound.worst_case_leak_rate_floor", "LeakyRateBound.exact_is_rate_zero", "LeakyRateBound.exact_floor_recovered", "LeakyRateBound.rate_floor_at_witness_params", "LeakyRateBound.rate_witness_concrete", "LeakyRateBound.drop_size_premise_fails", "LeakyRateBound.boundary_tight" ], "mirror_check": { "cells_premise_holds": 44, "cells_total": 48, "cells_violating_bound": 0, "note": "TRANSCRIPTION CHECK ONLY -- the Python mirror of maxFib agrees with the Lean prediction. NOT independent evidence for the theorem." }, "pass": true, "seed": 20260718, "trials_per_cell": 2000 }