{
  "claims": [
    "Theorem 3.7 proves an upper bound on excess risk of B_p* * B_X * M/sqrt(D) under an M-coverage condition on depth-D DAGs, extending networked information aggregation from squared loss to Binary Cross-Entropy-based binary classification (Theorem 3.7).",
    "Theorem 4.5 proves a matching lower bound showing instances with excess loss of at least Omega(k/D), where k is feature dimension and D is path depth, establishing network depth as a necessary bottleneck (Theorem 4.5).",
    "Lemma 3.1 establishes an orthogonality property of Binary Cross-Entropy residuals, E[x(p*(x)-y)] = 0, replacing the variance-decomposition tools used in prior squared-loss analyses (Lemma 3.1).",
    "Lemma 3.3 provides a KL/Bregman-type loss decomposition L(q) = L(p*) + D(p*||q), used with Pinsker-style bounds to connect BCE progress to prediction error (Lemma 3.3).",
    "The protocol models a sequential DAG in which each agent observes only a subset of features, receives parent logits (not probabilities), and locally minimizes Binary Cross-Entropy before passing its own logits downstream (Section 2)."
  ],
  "formula_summary": {
    "all_positive": true,
    "cells": 72,
    "depth_exponent_minus_one_half": true
  },
  "gates": {
    "all_logit_losses_nonincreasing": true,
    "all_m_coverage": true,
    "all_pinsker_certificates": true,
    "all_upper_bound_certificates": true,
    "bce_kl_decomposition_exact": true,
    "five_exact_claims_present": true,
    "formula_bounds_positive": true,
    "formula_panel_complete": true,
    "lower_bound_coefficients_valid": true,
    "lower_bound_excess_positive": true,
    "lower_bound_panel_complete": true,
    "lower_bound_scaled_constant_positive": true,
    "nonoptimal_reference_control_fails": true,
    "orthogonality_panel_complete": true,
    "orthogonality_residual_small": true,
    "positive_probability_control_gap": true,
    "probability_passing_control_worse": true,
    "protocol_panel_complete": true,
    "source_archive_pin": true,
    "source_pdf_pin": true,
    "source_scope_rows_complete": true,
    "upper_depth_exponent_minus_one_half": true
  },
  "lower_bound_summary": {
    "all_coefficients_in_open_unit_interval": true,
    "all_excess_positive": true,
    "cells": 56,
    "maximum_scaled_excess_D_over_k": 0.099745574981,
    "minimum_scaled_excess_D_over_k": 0.049078635566
  },
  "orthogonality_summary": {
    "all_pinsker_certificates": true,
    "cells": 24,
    "maximum_absolute_decomposition_gap": 0.0,
    "maximum_orthogonality_residual": 0.0,
    "nonoptimal_reference_counterexamples": 24
  },
  "paper": {
    "arxiv": "2605.01082v1",
    "openreview_id": "mrtg4NmvAe",
    "title": "Networked Information Aggregation for Binary Classification"
  },
  "passed": true,
  "protocol_summary": {
    "all_logit_losses_nonincreasing": true,
    "all_m_coverage": true,
    "all_upper_bound_certificates": true,
    "cells": 48,
    "mean_probability_control_excess_gap": 0.00618226885,
    "probability_control_worse_cells": 48
  },
  "scientific_scope": {
    "decomposition": "The BCE/KL identity requires the optimal same-feature-space logistic reference.",
    "matching": "The source uses matching for the depth bottleneck; upper and lower exponents are not identical.",
    "protocol": "The source transmits logits rather than probabilities."
  },
  "source_checks": {
    "pdf_sha256": "ca7263e8fd591b27cbd3f869d93ffe1818af27baaa439f278a27a5248ddd92b7",
    "source_sha256": "d17612d6f31795fe581812dd7e20bf00ce5fabc7408e61411b439232b9917417"
  }
}