The Observation → Continuation Principle: Why Persistence Requires Structural Registration in the Paton System

This paper introduces the Observation → Continuation Principle within the Paton System. The principle states that recursive system persistence requires the observational registration of admissible states. While admissibility determines which states are permitted to exist within a system, continuation across time requires those states to be registered within the observation interface. Observation therefore provides the structural reference through which recursive continuation becomes possible. The principle clarifies the relationship between observation and persistence across physical, computational, biological, and cognitive systems.