Admissible Trajectories Structural Motion Through Constraint Space

This paper introduces Admissible Trajectories within the Paton System as a structural description of system motion through constraint space. Building on the Admissibility Field Viability Gradient and Admissibility Curvature the framework defines admissible trajectories as paths through state space that remain entirely within admissible regions. This establishes a path based extension of admissibility analysis enabling examination of reachability stability evolution and collapse dynamics. The approach provides a domain independent method for analysing system motion without modifying underlying governing equations.