Phase-Space Admissibility Geometry

This paper interprets phase space through the admissibility framework of the Paton System. Traditional dynamical systems describe evolution as trajectories through phase space defined by system variables and their derivatives. The admissibility interpretation recognises that only states satisfying governing constraints are structurally permitted to exist within this space. Phase space therefore represents the geometric structure of admissible state evolution under system constraints. Trajectories correspond to admissible continuations through this constrained manifold. This interpretation clarifies the geometric character of dynamical stability, attractors, and invariant structures observed across physical, mathematical, and computational systems.