Structural Closure and Admissibility in Physical Theory: Closure Completeness and Paradox Impossibility

This work develops the structural consequences of the Closure Admissibility Principle (CAP), a constraint-based framework for analyzing the internal consistency of physical descriptions across quantum theory, spacetime models, and information-theoretic formulations. We formalize closure completeness, admissible observer classes, refinement stability, and irreversible operations, and demonstrate that paradox-generating constructions arise from structurally forbidden transformations rather than physical inconsistency. The paper proves a closure trichotomy governing admissible physical claims and establishes conditions under which apparent contradictions reduce to violations of admissibility constraints. Canonical examples from irreversibility, information flow, and foundational physics are analyzed within a unified operator-structural setting.