[
  "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)."
]