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.