Future 6G networks will rely on Large Language Model (LLM) agents to manage the Radio Access Network (RAN). However, current architectures assume inter-agent messages convey objective facts. A message is instead a \emph{trace} of the sender's reasoning: it carries a subjective conclusion, so a syntactically valid report can propagate an AI hallucination and trigger a cascading outage invisible to protocol validation. Reading such a trace requires a Theory of Mind (ToM)---before acting, the receiver must model what the peer believes, and what a peer in that position should have believed. Modeling these interactions as cognitive channels on a cellular sheaf, we obtain a unified framework for resilient multi-agent systems, from which five design principles emerge: (i) a message is evidence of the sender's hidden reasoning; (ii) trust is a continuous cognitive Signal-to-Noise Ratio (SNR)---asserted precision over deviation from the modeled peer belief; (iii) network-wide consistency and resistance to hallucination contagion are computable via the sheaf's Laplacian; (iv) peer-modeling must halt at exactly two levels to conserve compute and survive mutual information decay; and (v) credible capacity is bounded by operational goal alignment, not link bandwidth. A signaling-storm study on locally deployed 1B-parameter telecom language models validates it: cognitive SNR isolates a hallucinating peer that three of its four neighbors agree with, where a divergence gate ranks every wrong peer above the right one; only depth two ToM recovers the correct action; and the spectral gap decides whether a topology reaches consistency inside the near-real-time budget.

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