The Local Stability Theorem and the Structural Limits of Coherence: From Biological Regulation to Architectural Phase Transitions

We derive a general bound on sustainable informational coherence in suppressive environments. If environmental dynamics inject entropy at rate λ and a system maintains coherence through bounded control effort K, then steady-state mutual information satisfies I∞ ≤ K/λ. This establishes a hard ceiling on sustainable correlation between subsystems under persistent suppression. We extend this result in three directions: (1) a biological interpretation defining health as operation within the stability region K ≥ λI, with disease corresponding to departure from this region; (2) a non-local navigation extension modelling coherence between internal state and distant reference under latency and drift; and (3) a Mutualism Theorem introducing environmental coupling, yielding a phase transition from bounded regulation to architectural stabilisation when control effort modifies suppression itself. The framework unifies biological maintenance, engineered systems, and ecological niche construction under a single structural law. Linked empirical protocols test transcriptomic entropy as a cross-disease marker for coherence loss across sixteen conditions. Pre-registration. Analysis not yet conducted. All materials open access.