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.
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.
Foundational problems in physics—including quantum measurement, spacetime emergence, gravitational dynamics, nonlocality, the arrow of time, and the status of physical existence—are typically addressed in isolation, via model-dependent extensions or interpretive assumptions. This work proposes a different approach. We introduce a constraint-based framework, the Closure Admissibility Principle (CAP), which specifies minimal structural conditions any physical description must satisfy in order to be globally consistent. CAP is formulated in operational terms, using admissibility of states, recoverability under refinement, and stability of closed records, without assuming spacetime, dynamics, or ontology a priori. We show that enforcing these constraints induces a unifying closure structure on law-space, from which several persistent foundational puzzles are resolved as structural consequences rather than postulates. In particular, collapse is reclassified as record selection, spacetime and gravity emerge only in compressible regimes, General Relativity appears as an infrared universality class rather than a fundamental law, singularities correspond to failures of admissible description, and null (“nothing”) models are excluded as inadmissible fixed points. The framework is explicitly falsifiable via operational and weak-field tests, and its scope and limits are stated precisely. The results suggest that many foundational paradoxes arise not from incomplete dynamics, but from admitting globally incoherent physical descriptions.
This work presents a continuous, constraint-based interpretive framework for physical systems that unifies quantum behavior, classical structure, and cosmological evolution without introducing new forces or modifying established equations. Rather than treating quantum mechanics, electromagnetism, and general relativity as fundamentally separate domains, the paper proposes that these regimes can be understood as consistent descriptions of a shared underlying structure. The framework is built on three foundational elements: a non-geometric substrate (P_0) defining admissible configurations, interaction as the propagation of constraint, and geometry as the macroscopic record of accumulated interaction. Within this perspective, physical structure emerges through a continuous progression: distinctions enable gradients, gradients enable interaction, interaction accumulates as constraint, and constraint stabilizes into persistent configurations. The quantum–classical transition is interpreted as a continuous increase in interaction-induced constraint, while spacetime curvature reflects the large-scale organization of these interactions. The framework does not replace existing theories, but instead provides a unified conceptual interpretation that remains fully consistent with established physics across known regimes. Its value lies in clarifying relationships between domains, offering a continuous ontology of physical systems, and suggesting potential directions for further formalization.
We propose a constraint-based formalism in which physical systems are characterized by operators acting on a state space. In this framework, constraint operators encode admissibility, projection, and structural restriction in a unified manner. We analyze the algebraic properties of these operators and show that, under natural conditions, they form a projection-based structure. This perspective provides a common structural language that accommodates diverse physical theories. In particular, projection operators in quantum mechanics may be interpreted as instances of constraint operators, and measurement processes may be viewed as constraint-driven transformations. In statistical and information-theoretic contexts, entropy can be interpreted as a coarse-grained measure of the size of constraint-compatible state spaces. The proposed formalism does not aim to replace existing theories, but to provide a minimal and theory-independent framework for describing how physical structure may arise from constraints. This work provides a structural bridge between constraint-based formulations and projection structures in quantum mechanics.
Physical theories constrain systems through equations of motion, symmetries, boundary conditions, and variational principles. In many cases these constraints do not uniquely specify a single trajectory or configuration, but instead permit a family of admissible histories consistent with the same governing structure. This multiplicity is often treated implicitly, absorbed into formalism, or deferred to probabilistic interpretation. In this work, I introduce allowity as a diagnostic concept that characterizes the effective extent of admissible histories implied by a set of constraints, prior to any statistical weighting, measurement, or interpretation. Allowity is not randomness, uncertainty, freedom, or ignorance; it is a structural property of constraint-based descriptions. By making admissibility explicit, this framework clarifies how physical descriptions may remain stable despite non-uniqueness, or become brittle despite apparent determinism. The analysis is conservative and framework-neutral: it introduces no new dynamics and modifies no existing formalism.
We present a minimal structural framework in which relativistic causality and quantum probability emerge as effective descriptions, without postulating spacetime geometry, dynamical equations, or quantum states as primitives. The framework is based on resolution-dependent representations and an accounting invariant that tracks irreducible loss under coarse-graining. Crucially, we do not propose an alternative formulation of quantum mechanics, but identify minimal structural constraints under which any admissible physical theory must reduce to probabilistic descriptions. We show that locality and closure of admissible updates force causal cone structures and probabilistic state updates. Classical spacetime dynamics, such as General Relativity, can be understood within this framework as selected realizations that satisfy the same admissibility constraints under appropriate resolution regimes. Rather than competing with existing physical models, this theory constrains which models are physically admissible.
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/