The Paton System — A Structural Architecture of Admissibility, Recursion, and Continuity

This paper presents the Paton System as a unified structural architecture governing system existence, continuation, and observation. Admissibility is established as the pre-theoretical condition for system membership, enforced at Tier 3 through the Paton Admissibility Test. Recursive continuation, expressed at Tier 5, operates only under admissibility constraint, forming a recursively gated system. Across the full tier structure Tier 0 to Tier 8, possibility expands and is subsequently filtered, producing observable structure as a constrained projection rather than a complete representation of total possibility. Continuity arises through the persistence of admissible recursion across all tiers. The framework formalises three core relationships: Admissibility as the condition of existence Recursion as the mechanism of continuation Observation as the projection of admissible structure It introduces a convex to concave structural transformation in which possibility expands at Tier 2, is filtered at Tier 3, and resolves into observable structure at Tier 4. The system is shown to be recursively gated at every transition, with no unrestricted propagation. This work provides a domain-neutral structural architecture applicable across physical, biological, computational, and cognitive systems, without introducing new domain-specific laws. It operates as a pre-theoretical admissibility layer governing whether systems may exist and persist prior to explanation or modelling.