Phase transitions in the functional connectivity of semantic agent networks under local filtering constraints

We apply statistical physics methods to model the stability of decentral ized agent networks. Mapping the problem to bond percolation on complex directed graphs, we show that strictly enforcing local semantic constraints induces a sharp global phase transition, characterized by the sudden collapse of the giant strongly connected component (GSCC). We identify the GSCC fraction as the functional connectivity order parameter (Sfunc) that governs macroscopic system coordination. Our results demonstrate that this transition occurs at a specific critical strictness threshold θ*, which shifts exponentially with the semantic complexity of transmitted message bundles. This behavior is robust across Erdos-Renyi, Barabasi-Albert, and Stochastic Block Model topologies, suggesting that semantic collapse is a universal feature of decen tralized filtering systems. We further analyze mitigation strategies from a critical phenomena perspective, showing that near the critical point, purely local relaxation protocols fail, while hub-targeted interventions successfully restore connectivity. These findings provide a statistical physics basis for understanding the stability limits of decentralized semantic networks.