The Structural Continuation Theorem: A Unified Persistence Rule in the Paton System

This paper introduces the Structural Continuation Theorem within the Paton System. The theorem states that a system state can participate in recursive continuation only if it is both structurally admissible and observationally registered. By combining the Admissibility → Observation Theorem and the Observation → Continuation Principle, the theorem defines the minimal structural condition required for persistence within a system. The result provides a unified rule describing how systems form observable histories and maintain structural continuity across time.