Observation as a Gate of Continuation: Registration as the Condition of Persistence Within the Paton System

This paper establishes the structural relationship between observation and continuation within the Paton System. It demonstrates that persistence depends on structural registration rather than admissibility alone. Observation is defined as the mechanism by which admissible states become registered and available for continuation. Only registered states can propagate forward within a system, while unregistered states remain unresolved and unavailable for persistence. This clarifies the role of observation as an active boundary process governing continuity across physical, computational, biological, and cognitive domains.