The Admissibility Framework: Scope, Limits, and Consequences

This paper consolidates and bounds an admissibility-based framework developed across a sequence of prior works. Admissibility was introduced as a structural restriction on realizable trajectories, inducing a closure operator on state space and an associated order on admissible-closed sets. From this structure, scalar quantities including admissibility depth and admissibility entropy were defined, and the evolution of entropy under admissible dynamics was classified. The present work summarizes these results, states explicitly what has and has not been established, and identifies failure modes and falsifiability conditions for the framework. No new definitions or theorems are introduced. No physical laws, experimental claims, or interpretations are asserted. This paper serves as a synthesis and boundary statement for the admissibility framework, clarifying its scope, consequences, and limits as a structural constraint on dynamics.