The Tier-5 Recursive Continuation Engine: Structural Persistence in the Paton System

This paper formalises Tier-5 of the Paton System: the recursive continuation engine responsible for the persistence of admissible structures. After states pass the Tier-3 admissibility gate and become observable through the Tier-4 datum interface, continuation requires a generative process capable of maintaining structural compatibility across time. Tier-5 represents this recursive machinery. The paper clarifies the relationship between admissibility, observation, and continuation and explains how recursive persistence arises from constraint-compatible structural repetition. Within the Paton System architecture, earlier tiers describe the formation and filtering of system states through distinction, constrained flow, and admissibility gating. Tier-4 registers admissible states through the observation interface. Tier-5 then governs whether these states persist through recursive compatibility with governing constraints. The paper introduces the concept of recursive continuation as a structural requirement for persistence across domains including physics, computation, biology, and cognition. Systems continue only while successive states remain admissible relative to their governing constraints. By formalising the recursive continuation engine, this work clarifies the generative persistence mechanism operating within the Paton System architecture.