Unified Admissibility Theory A Constraint-Geometric Framework for Physical, Quantum, and Computational Systems

We introduce a unified framework in which system validity, dynamics, and evolution are governed by constraint-defined admissibility. A system state is admissible if it satisfies a set of constraints, and deviation from admissibility is quantified by a residual function α(S). We show that system evolution can be expressed as a gradient-driven process minimizing α(S), providing a unified description of physical motion, computational optimization, and control systems. We further extend the framework to a variational formulation and demonstrate that α(S) acts as a generalized potential. A quantum formulation is derived in which α(S) appears as a constraint-based potential term in the Schrödinger equation. Measurement is interpreted as constraint injection, and apparent probabilistic behavior emerges from admissibility structure. The theory provides a unified description across classical mechanics, quantum systems, and computational processes, reframing dynamics as the minimization of inconsistency with respect to constraint-defined admissibility.