Wrong consensus in LLM swarms becomes unreachable once each agent reads fewer than 6.4 messages

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arXiv 2609.19183 (submitted 2026-09-15) reduces how many of the others' contributions an agent reads to one number, message capacity, and generates the communication network from it. Across 31,824 randomized queries, an 8B model's judgment of a claim reduced to a logistic function of a weighted sum of its inbox, the update rule of a stochastic binary neuron with divisively normalized weights. From those weights and the network degree statistics alone, wrong consensus becomes unreachable from any starting state once agents read on average fewer than 6.4 of the others' messages. That is a tunable design parameter for anyone wiring a multi-agent debate loop.