The Paton System: A Unified Structural Framework for Admissibility, Observation, and System Continuation

The Paton System is a structural framework that determines when systems are permitted to exist, be observed, and persist prior to domain-specific modelling. While previous work has formalised individual components of the framework—including admissibility, observation, continuation, persistence, recursion, and termination—these elements have not yet been presented as a unified architecture. This paper synthesises those components into a single structural framework describing the lifecycle of systems across domains. The framework defines the minimal conditions under which states may belong to a system, become observable, propagate through continuation, persist across time, and terminate when no admissible continuation paths remain. The resulting architecture provides a domain-neutral admissibility filter applicable across physical, biological, computational, and organisational systems. By unifying previously established results within the Paton System research programme, the paper provides a single reference overview of the structural architecture governing system existence.