Admissibility as a Structural Constraint on Dynamics

This series develops an admissibility-based framework in which admissibility is treated as a structural restriction on realizable trajectories rather than as a modification of equations of motion. The work proceeds by defining admissibility as a closure operator on state space, inducing an order and lattice structure on admissible-closed sets. From this structure, scalar quantities including admissibility depth and admissibility entropy are defined. The series is organized in three stages. The first set of papers establishes the admissibility operator, the induced closure, order, and lattice structure, and the associated scalar quantities. The second set examines the behavior of these quantities under admissible dynamics, including classification of entropy evolution. The final papers record conditions under which admissibility entropy may be interpreted physically and consolidate the framework by explicitly stating its scope, limits, and falsifiability conditions. All results are structural and conditional. No physical laws, experimental claims, or interpretations are asserted. The purpose of the series is to provide a disciplined mathematical framework that constrains realizable trajectories and derives consequences of that constraint alone, prior to any physical specialization.