{
  "all_gates_pass": true,
  "arxiv": "2605.20696v1",
  "gates": {
    "all_outputs_finite": true,
    "claim1_actual_feddpo_executed": true,
    "claim1_inverse_S_terms_exact": true,
    "claim1_partial_bound_multiple_E_S_R": true,
    "claim2_full_participation_amplification_removed": true,
    "claim2_residual_client_average_variance_preserved": true,
    "claim3_stale_algorithm_executed": true,
    "claim3_staleness_formula_exact": true,
    "claim3_staleness_zero_at_q_zero": true,
    "claim4_full_participation_sampling_variance_zero": true,
    "claim4_lower_bound_scaling_exact": true,
    "claim5_connectivity_factor_varies": true,
    "claim5_decdpo_executed": true,
    "claim5_four_symmetric_graphs": true,
    "claim6_all_four_ablation_families": true,
    "claim6_exact_N5_times_120_SHP_rows": true,
    "destructive_identical_clients_reduce_participation_effect": true,
    "destructive_label_corruption_worsens_clean_objective": true,
    "destructive_no_mixing_increases_consensus_error": true,
    "source_pins_verified": true
  },
  "headline": {
    "clean_final_loss": 0.670980521644771,
    "clients": 5,
    "decdpo_algorithm_runs": 32,
    "decdpo_topology_cells": 4,
    "fed_ablation_cells": 9,
    "fed_ablation_ranges": {
      "local_steps": 0.0001053080043843886,
      "participation": 1.7833669850922645e-07,
      "staleness": 4.7174168747956885e-05
    },
    "fed_algorithm_runs": 72,
    "identical_client_S1_to_S5_ratio": 1.0004384715044146,
    "kappa_squared": 0.001157812224058244,
    "label_corrupted_final_loss": 0.690625282427891,
    "lower_bound_cells": 20,
    "no_mix_to_mix_consensus_ratio": 575.6464809616402,
    "pairs_per_client": 120,
    "shp_pairs": 600,
    "smoothness_L_bound": 0.04000000000000001,
    "staleness_formula_cells": 15,
    "theorem_5_1_formula_cells": 36,
    "topology_consensus_range": 0.0005454370424672539,
    "topology_factor_consensus_spearman": 1.0,
    "zeta_squared": 0.039387909241610605
  },
  "openreview_id": "ljNZyrAlaa",
  "paper": "Distributed Direct Preference Optimization",
  "scope": "finite log-linear SHP mechanism audit plus exact source-formula reconstruction",
  "seed": 20260721
}