From Admissibility to Motion: Constraint as the Origin of Dynamics Within the Paton System

This paper establishes the structural relationship between admissibility and motion within the Paton System. It shows that motion arises only within admissible regions defined by constraint and is not a fundamental primitive. Motion is reframed as traversal within admissible space, with all trajectories bounded by viability and constraint compatibility. This clarifies the origin of dynamics across domains without modifying existing physical or mathematical laws.