6G Reasoning Agent Societies: Composition, Scaling, and Consistency-Time Laws

Abstract

Emerging 6G control planes would compose Large Language Model (LLM) agents that exchange interpreted conclusions, so hallucinations can propagate even over error-free transport. Recent architectures audit each message locally against the sender's observation mask, but isolated audits miss collective behavior. Modeling the agent society as a cellular sheaf, we establish three laws valid on arbitrary topologies. First, the \emph{composition law}: network-wide divergence exceeds the sum of per-agent audit scores by exactly their hidden total correlation. This blind spot masks up to 23\% of joint divergence and, because the declared signal cancels in the cognitive signal-to-noise ratio (SNR), overstates it by $1.14$\,dB purely through topology; the resulting trust inflation preserves valid consensus states but slows convergence. Second, the \emph{scaling law}: reconciliation decouples across metric counters, so the worst-connected dimension sets the pace. Consistency time grows for a society size $n$ as $Ω(n^{2/d})$ on polynomial-growth topologies of degree $d$, and paths breach a $1$\,s near-real-time budget at $n^\ast=13$ agents, whereas expanders ($Θ(1)$) and radius-3 local audits ($O(1)$, $\approx300$\,ms) stay bounded. Third, the \emph{consistency-time law}: the timing error from omitted correlations is one-sided and capped by the worst-measured link. These laws, validated on simulated topologies and deployed LLM societies, give provable worst-case latency ceilings for near-real-time operation.