The Coherence Ratio R★ as a Cross-Domain Marker of Self-Stabilizing Systems

Systems across physical, biological, and cognitive domains remain stable when internal processes restore their configuration more rapidly than external forces introduce variation. This paper develops a general coherence threshold that identifies the moment a system begins to maintain its own pattern across time. The threshold is expressed by the ratio R = (τ_self⁻¹) / Γ_disruption and the critical value R★ at which restoration becomes sufficient to support a persistent interior. The threshold applies independently of material substrate and identifies a structural condition that appears in lipid boundaries, recurrent neural circuits, and distributed cognitive processes. The paper outlines specific predictions that follow from the threshold and describes how these predictions may be evaluated through experiments in neuroscience, cognitive science, and biological organization. The coherence threshold also aligns with and extends existing approaches to consciousness, including integrated information theory, active inference, and dynamical systems models. This framework offers a concise and general account of when a system begins to hold its configuration across time and how this condition supports interiority, binding, and awareness.