Resonant Persistence in Non-Stationary Environments: A Stability Framework for Sustained Informational Coherence

We derive a general stability inequality governing the preservation of mutual information between a system and a reference under environmental suppression: I∞ ≤ K/λ. We extend this foundational bound in three directions. First, to non-stationary environments where suppression varies over time, deriving the condition under which adaptive bandwidth growth maintains stability. Second, to nonlinear environmental coupling, where control effort modifies suppression itself, yielding a bifurcation threshold (K_c = λ₀/α) that separates bounded regulation from architectural stabilisation — a phase transition from systems that resist their environment to systems that reshape it. Third, to collective oscillator synchronization via Kuramoto dynamics, showing that the same K/λ structure governs ensemble phase coherence with coupling strength as collective bandwidth and noise amplitude as collective suppression. The framework unifies results from control theory, information theory, nonlinear dynamics, and collective synchronization under a single structural law. A clearly separated interpretive appendix explores implications for biological regulation, adaptive resilience, and the architecture of persistent organisation. This paper extends the Local Stability Theorem (linked companion, OSF) from a static bound to a full dynamical framework. All formal claims are technical and bounded. No violation of thermodynamic laws or relativistic geometry is implied. Linked empirical programme tests transcriptomic entropy as a cross-disease coherence marker across sixteen conditions. Pre-registration. Analysis not yet conducted. Open access.