A Structural Theory of Admissibility

This paper proposes a structural framework in which physical laws and quantum probability emerge from a common admissibility principle, rather than from the unification of dynamical equations.No new forces, fields, particles, or dynamical laws are introduced.Instead, a universal structural constraint governing which states are admissible as physically realizable is identified. Building on results established in Admissibility Frameworks I and II, the existence of a universal frame constant limiting allowable transitions is taken as a starting point.From this principle, an equation of existence is formulated, which does not describe time evolution but instead delineates the boundary between admissible and non-admissible states.Different physical interactions are shown to correspond to distinct structural interpretations of the same admissibility condition. Within this framework, quantum states are interpreted not as probability amplitudes but as admissibility distributions.Measurement is described as structural filtering at the admissibility boundary, rather than as a dynamical collapse process.Under minimal and physically natural assumptions—phase invariance, orthogonal additivity, and locality—the admissibility measure is shown to be uniquely quadratic, yielding the Born rule as a structural consequence rather than a postulate. The resulting theory reframes unification as the closure of existence conditions shared by all physical theories.Dynamics remain domain-specific, but admissibility is universal.In this sense, unification is achieved not by combining forces, but by identifying the single structural condition under which any physical state may exist. AI Usage Declaration: The core concepts and mathematical intuitions of this paper were conceived by the author (Byeong-Young Oh). The technical formalization of the mathematical framework and the English drafting process were performed in collaboration with Artificial Intelligence (AI) models. The author takes full responsibility for the contents and logical integrity of this work. This work is part of an ongoing independent research program. Official research index :https://jingyu-papa.github.io/publications/