The Paton System: A Unified Architecture of Admissibility and Continuation

This paper presents the Paton System as a unified structural architecture governing system membership, persistence, and continuation prior to domain-specific modelling. Most scientific frameworks implicitly assume valid system states before equations, simulations, or optimisation procedures are applied. The Paton System instead formalises the minimal structural conditions required for system membership. The framework is organised into layered tiers beginning with availability, distinction, and constrained relation, progressing through an admissibility gate and datum interface, and extending into generative machinery, structural laws, and cross-domain instantiations. The central rule states that a state belongs to a system if and only if it is both admissible and reachable: it must satisfy governing constraints and lie on at least one admissible trajectory from a permitted origin. This architecture clarifies how persistence and collapse arise as consequences of constraint compatibility rather than domain-specific mechanisms. The Paton System therefore functions as a domain-neutral pre-theoretical framework applicable across mathematics, physics, computation, biological systems, and organisational dynamics.