We introduce a minimal formal framework for encoding distinction without presupposing time, dynamics, refinement, interpretation, or representation. The framework consists of a carrier equipped with a primitive relation,interpreted minimally as distinguishability. Collapse is defined as the absenceof all distinction. We isolate non-collapse as a boundary condition and showthat, by itself, it entails almost no structure. We then introduce a singleadditional notion—admissible weakening—and prove that non-collapse ispreserved under admissible weakening if and only if at least one distinctionis irreducible. This establishes the minimal structural content forced byexclusion of collapse, without introducing dynamics, laws, or domain-specificassumptions.
We introduce a minimal formal framework for encoding distinction without presupposing time, dynamics, refinement, interpretation, or representation. The framework consists of a carrier equipped with a primitive relation,interpreted minimally as distinguishability. Collapse is defined as the absenceof all distinction. We isolate non-collapse as a boundary condition and showthat, by itself, it entails almost no structure. We then introduce a singleadditional notion—admissible weakening—and prove that non-collapse ispreserved under admissible weakening if and only if at least one distinctionis irreducible. This establishes the minimal structural content forced byexclusion of collapse, without introducing dynamics, laws, or domain-specificassumptions.
Abstract We investigate the minimal structural conditions under which representational accessibility and irreversibility-like asymmetry arise in physical description. Starting solely from the existence of distinguishable states and a class of admissible transformations, we analyze how accessibility of distinctions changes under non-injective representational updates without introducing prior notions of space, time, probability, measurement, or thermodynamic structure.Admissible non-injective transformations naturally induce equivalence relations on the state space, leading to a distinction between manifest difference, corresponding to representationally accessible distinctions, and latent difference, corresponding to distinctions that remain structurally present but inaccessible within a given representation. We show that accessibility and recoverability of distinctions are determined intrinsically by the admissible transformation structure itself rather than by externally imposed observational limitations or representational scales.A central result of the framework is that irreversibility-like asymmetry arises when latent distinctions become non-recoverable within the admissible transformation class. In this perspective, irreversibility-like behavior is interpreted not as a consequence of probabilistic uncertainty or thermodynamic entropy increase, but as a structural restriction on recoverability of representational accessibility.The present work does not introduce new mathematical constructions. Rather, it provides a conceptual reinterpretation of equivalence structures, representational accessibility, and recoverability within a minimal framework of physical description. This framework identifies structural preconditions for accessibility restriction and recoverability failure prior to the introduction of statistical, thermodynamic, or observer-dependent assumptions.
Abstract This paper proposes a minimal formal criterion for physical entity. It does not attempt to derive quantum mechanics, general relativity, quantum gravity, or any empirical prediction. Its aim is narrower: to ask what formal conditions must be satisfied before a structure may be treated as a physical entity at all. The starting point is the principle of stable distinguishability: a physical theory is possible only where distinctions can be made and re-identified under admissible change. From this requirement, the paper develops a constraint-primacy framework in which no particle, field, spacetime point, state, measurement, or observable is assumed as primitive. The formal layer consists of tokens, admissibility, and a closure operator defined on the full power set of tokens. Identity is reconstructed as closure-equivalence. Boundary is defined non-spatially as first-entry dependency, and core is defined non-circularly as a closed non-boundary substructure. A physical entity is then defined as a boundary-stable closure-core equivalence class: a closed admissible structure whose core closure-identity is preserved under relevant boundary-mediated extensions. The paper uses familiar mathematical tools, including closure, equivalence, isomorphism, and invariance; its proposed contribution is not those tools themselves, but the ontological criterion they support.
This paper establishes a minimal formal foundation for structure under irreversibledistinguishability. Starting from a single primitive—distinction—we derive equivalence,refinement, irreversible loss, persistence, probability, Hilbert space structure, unitaryadmissible transformations, counting, and intrinsic temporal ordering. No physical,probabilistic, or dynamical axioms are assumed. Probability, time, and reversible evolution arise necessarily as constrained structures induced by unresolved refinement andirreversible elimination. The formal core is shown to be minimal, irreducible, andcomplete with respect to admissible structure under loss. This paper constitutes thefoundational core of a multi-paper series deriving physics, chemistry, biology, cognition,and society as successive constrained extensions of irreversible distinguishability.
AbstractWe investigate the minimal structural conditions under which relational accessibility organization admits a topological representation within physical description. Starting solely from the existence of distinguishable states and admissible comparison relations, we analyze how accessibility structures arise without introducing prior notions of space, geometry, metric structure, probability, or dynamics.Within the present framework, comparison between states is interpreted as a structural relation governing the accessibility of distinctions. The consistency requirements imposed on admissible comparisons induce preorder-like relational organization on the state space. We show that such comparison-induced accessibility structures admit neighborhood-like representations and may be organized in a form compatible with topological description.Importantly, the present framework does not interpret topology as a primitive geometric entity. Rather, topological structure is treated as a mathematical representation of relational accessibility induced by admissible comparison structure. In this perspective, neighborhood relations characterize accessibility coherence among distinguishable states rather than spatial proximity in a preexisting geometric manifold.We further show that equivalence structures associated with comparison naturally introduce classes of states that are indistinguishable within a given accessibility framework while remaining structurally distinct in the underlying state space. This provides a relational interpretation of local accessibility organization without invoking observer-dependent notions or externally imposed representational scales.The present work does not introduce new mathematical constructions. Instead, it identifies structural conditions under which topological representation becomes compatible with a minimal relational framework of physical description.
This work proposes the Negative Representation Principle, a conceptual framework in which observable reality is interpreted as the distinguishable resolution of an underlying state of total indistinction. The fundamental state, denoted by I, is not empty nothingness but maximal coincidence, in which no difference is resolved. The observable universe U is defined as a representational relation U ≡ N(I), where distinction becomes structurally resolvable. Within this framework, no information is created. Distinction does not generate content but makes it observable. Space, time, and matter are interpreted as properties of distinguishability: space as relational structure, time as ordered distinction, and matter as stable configurations of difference. The model excludes selection, probability, and causal origin at the fundamental level. Instead, stable structures arise as a consequence of structural consistency: only those representations in which distinctions are non-contradictory, mutually compatible, and relationally closed can persist. Multiple representations are admissible, but not coexistent within a single distinguishable reality. The observed universe is not selected among possibilities, but is the one in which structural consistency allows observation to occur. This work is intended as a foundational conceptual contribution, at the intersection of physics and philosophy, aimed at clarifying the role of distinction in the structure of observable reality.
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/