The Paton System: A Structural Framework for Stability, Persistence, and Collapse Across Complex Systems

Scientific disciplines typically analyse systems through domain-specific mechanisms, equations, or models. However, systems across many domains exhibit similar structural patterns governing stability, persistence, and collapse. The Paton System proposes a structural framework that precedes domain-specific modelling. It identifies admissibility as the condition governing whether system states are permitted to persist and generate valid continuation. Within this framework, systems remain stable while their internal states remain compatible with governing constraints that define admissible state transitions. The Paton System provides a layered architecture describing how systems emerge, become observable, generate behaviour, and persist within constraint-defined regions of stability. The framework introduces a structural hierarchy beginning with undivided structural availability, progressing through distinction, formation, admissibility, observation, generative continuation, and structural laws governing persistence. Domain-specific systems appear as instantiations of these structural principles. By identifying admissibility and constraint compatibility as the conditions governing system persistence, the Paton System offers a unified structural perspective on stability and collapse across complex systems in engineering, biology, economics, and network infrastructures.