A recurring interpretive move in quantum physics treats the loss of observational distinguishability as equivalent to the loss of ontological structure. In this paper, I show that the formal structure of the theory does not support that move. I prove the Structural Persistence Theorem, which identifies precisely which algebraic invariants survive arbitrary completely positive trace-preserving (CPTP) maps. The invariants form a natural and complete set: the C*-algebra of observables A = B(H), its norm, commutation relations, and positivity structure. No CPTP process removes any observable from the algebra. State-space distinguishability contracts; algebraic structure does not. This partition — preserved structure versus contracted epistemic access — is the core formal result of the paper. I identify and formally diagnose a specific class of ontological overclaiming in the decoherence literature: instances where pointer-basis selection and suppression of off-diagonal density matrix elements are treated as eliminative of superposition. I show exactly where these inferences overreach the formalism and provide corrected formulations. I then demonstrate that this criterion places formal constraints on how the major quantum interpretations can consistently attribute ontological change. Many-Worlds and pilot-wave theory are fully consistent with the criterion. Copenhagen's physical-collapse reading carries an unspecified mechanism burden. GRW and CSL objective collapse models are PC-violating by deliberate design — which the framework clarifies rather than criticizes. Any empirical confirmation of GRW/CSL predictions would constitute direct evidence for PC-violation in nature. Two practical applications are discussed. In quantum error correction, the success of the fault-tolerance threshold theorem is indirect empirical evidence for the Persistence Criterion: decoherence degrades distinguishability but leaves the algebraic structure intact, which is precisely what makes error recovery possible. In effective field theory, the persistence of UV degrees of freedom under coarse-graining is consistent with the same structural partition. This work proposes no new experimental predictions. It clarifies what the existing formalism entails and does not entail — drawing a sharp, formal boundary between what the mathematics licenses and what must be supplied by interpretation.
A recurring interpretive move in quantum physics treats the loss of observational distinguishability as equivalent to the loss of ontological structure. In this paper, I show that the formal structure of the theory does not support that move. I prove the Structural Persistence Theorem, which identifies precisely which algebraic invariants survive arbitrary completely positive trace-preserving (CPTP) maps. The invariants form a natural and complete set: the C*-algebra of observables A = B(H), its norm, commutation relations, and positivity structure. No CPTP process removes any observable from the algebra. State-space distinguishability contracts; algebraic structure does not. This partition — preserved structure versus contracted epistemic access — is the core formal result of the paper. I identify and formally diagnose a specific class of ontological overclaiming in the decoherence literature: instances where pointer-basis selection and suppression of off-diagonal density matrix elements are treated as eliminative of superposition. I show exactly where these inferences overreach the formalism and provide corrected formulations. I then demonstrate that this criterion places formal constraints on how the major quantum interpretations can consistently attribute ontological change. Many-Worlds and pilot-wave theory are fully consistent with the criterion. Copenhagen's physical-collapse reading carries an unspecified mechanism burden. GRW and CSL objective collapse models are PC-violating by deliberate design — which the framework clarifies rather than criticizes. Any empirical confirmation of GRW/CSL predictions would constitute direct evidence for PC-violation in nature. Two practical applications are discussed. In quantum error correction, the success of the fault-tolerance threshold theorem is indirect empirical evidence for the Persistence Criterion: decoherence degrades distinguishability but leaves the algebraic structure intact, which is precisely what makes error recovery possible. In effective field theory, the persistence of UV degrees of freedom under coarse-graining is consistent with the same structural partition. This work proposes no new experimental predictions. It clarifies what the existing formalism entails and does not entail — drawing a sharp, formal boundary between what the mathematics licenses and what must be supplied by interpretation.
This preprint introduces the Persistence Criterion (PC), a conceptual and mathematical framework for distinguishing epistemic obscuration from ontological elimination in physical theories. The central claim is that uncertainty, noise, decoherence, or coarse-graining reduce empirical distinguishability of states or observables without implying that the underlying theoretical structures cease to exist. The framework is developed across classical estimation theory, stochastic dynamical systems, and quantum theory. In the classical domain, noisy observation models and information-theoretic metrics are used to show how distinguishability contracts while state variables persist, consistent with standard treatments in estimation theory and statistical physics (e.g., Fisher information and Bayesian filtering). For dynamical systems, stochastic differential equations and Fokker–Planck dynamics illustrate how deterministic generators remain structurally present despite diffusion-dominated behavior, aligning with established results in open-system dynamics and control theory. In the quantum domain, the Persistence Criterion is formulated using density operators, completely positive trace-preserving (CPTP) maps, and the algebraic (C*-algebraic) formulation of quantum mechanics. Decoherence is treated as an obscuring process acting on states via CPTP channels, while the underlying observable algebra remains invariant. This formulation draws on standard results from quantum information theory and algebraic quantum mechanics, emphasizing that loss of coherence or distinguishability does not entail annihilation of observables or dynamical structure (Holevo, 2011; Nielsen & Chuang, 2010; Breuer & Petruccione, 2002). The Persistence Criterion is interpretation-neutral and consistent with quantum no-go theorems, including Bell, Kochen–Specker, and PBR-type results, as it makes no assumption of value definiteness or hidden variables. Instead, it functions as a criterion of ontological coherence, identifying and excluding a specific interpretational error: the conflation of indistinguishability with non-existence. The work is aligned with non-eliminative structural realism and contemporary discussions of decoherence and ontology in quantum foundations (Ladyman & Ross, 2007; Wallace, 2012; Ruetsche, 2018). No new physical dynamics or empirical predictions are proposed. The contribution is conceptual and formal: clarifying how existing mathematical frameworks already encode persistence under uncertainty, and providing a principled interpretational constraint applicable across classical and quantum theories.
This project presents a conceptual and mathematical investigation into the relationship between uncertainty, distinguishability, and the ontological persistence of physical variables. Rather than treating uncertainty as a mechanism that alters or destroys underlying system states, the work develops a formal framework in which uncertainty acts as an obscuring layer that limits epistemic access while leaving fundamental structure intact. Using tools from information theory, stochastic dynamics, and quantum state evolution, the study introduces a Persistence Criterion that distinguishes between genuine ontological change and mere loss of distinguishability. The framework is applied across classical noise models, feedback-controlled systems, and quantum decoherence processes to demonstrate that contraction of information measures does not imply elimination of underlying states. The project aims to clarify common interpretational confusions in physics and complex systems, particularly in contexts involving strong noise, coarse-graining, and measurement limits. It is intended as a foundations-oriented contribution, with relevance to physical modeling, control theory, and the philosophy of uncertainty.
Abstract We present Kunato Core Ver.5.0.0, a general framework for ontological admission, typed representation transport, empirical identifiability, effective-structure validation, and provenance-preserving epistemic state transition. The framework addresses a recurrent inferential problem across mathematical physics, statistical inference, inverse problems, effective theories, information theory, complex systems, quantum theory, and scientific realism: mathematical definability, empirical adequacy, model identification, and physical realization are distinct achievements and must not be silently promoted into one another. Kunato formalizes this separation through the constraint Formal(M) AND Emp(M; O) DOES NOT IMPLY Ontic(M). No representation receives automatic ontological privilege. Finite observation provides a first source of non-identification. Distinct formal models can agree exactly on a finite empirical record; in particular, uncountably many models can be constructed that coincide on any prescribed finite set of sample points. This establishes non-uniqueness within the relevant formal model class without promoting mathematical alternatives into claims about distinct physical causal histories. Finite measurement precision is treated through fibers of explicit resolution maps rather than by identifying metric neighborhoods with equivalence classes. The framework further distinguishes finite-dimensional state spaces from finite-state ontologies: finite-dimensional complex Hilbert spaces can contain a continuum of pure-state rays, whereas finite operational distinguishability requires additional assumptions such as a uniform positive separation scale on a compact state space. For stochastic observations, Kunato separates distributional identifiability, asymptotic inference, finite-sample discrimination, and zero-error identification. Positive overlap between competing observational laws prevents zero-error discrimination from the corresponding finite record. Increasing statistical evidence can therefore strengthen discrimination without automatically supplying an ontological realization warrant. Identification within a declared candidate class likewise remains conditional on that class and does not establish that physical reality belongs to it. The mathematical core is a typed property-transport calculus. Given a representation map Phi: X -> Y and a property P: X -> Z, P factors through Phi precisely when P is constant on every fiber of Phi. Equivalently, the kernel equivalence relation induced by Phi is contained in the kernel equivalence relation induced by P. This criterion separates state identification from property identification: a non-injective representation may fail to recover individual source states while still determining every property invariant on its fibers. Representation types, identified by their induced fiber equivalence relations, are organized by refinement within the complete lattice of equivalence relations on X. This provides a common mathematical structure for coarse-graining, quotient representations, projections, information loss, recoverability, and comparison of effective descriptions. Refinement is a partial order, so representations may also be incomparable. Effective structures consequently require property-specific transport warrants. Compression of a unitary parent operator, for example, need not preserve unitarity or normality. Conversely, non-normality alone does not entail a non-real spectrum, irreversibility, non-Markovianity, or absence of characteristic timescales. Observable symmetry, effective geometry, statistical regularity, entropy, information structure, temporal scales, and other representation-dependent properties cannot be transported automatically to a parent ontology. Kunato operationalizes these restrictions through methodological admission protocols. The Metric Admission Protocol regulates inference from effective metric structure to fundamental geometry. The Statistical-Invariant Admission Protocol separates existence of a mean from typicality, concentration, and self-averaging. The Timescale Admission Protocol distinguishes observed decay and hazard structure from claims about fundamental temporal dynamics. The Informational-Semantic Admission Protocol constrains inference from probability, entropy, information geometry, and semantic structure to latent ontology. The Criticality Admission Protocol separates phenomenological scaling from stronger claims of critical structure by requiring appropriately scoped diagnostics such as finite-size behavior, exponent stability, data collapse, robustness analysis, and negative controls. These protocols are methodological admission criteria rather than asserted laws of nature. Ontological admission is governed by differentiated semantic, fit, identification, scope, realization, revocation, and provenance warrants. These warrant types prevent empirical fit, interpretation, candidate-class identification, physical realization, and evidential history from being collapsed into an undifferentiated notion of support. Epistemic judgments are represented as contextual and versioned states, allowing changes in evidence, candidate classes, semantics, scope, and warrants to be reconstructed as explicit state transitions rather than hidden revisions. A central distinction is that UNRESOLVED is not REJECTED. Failure to establish an adequate promotion warrant blocks the requested inference but does not establish falsity or nonexistence. Rejection requires an independent refutation condition. Revocation acts on claims and accepted epistemic states while retaining their provenance; it does not imply any operation on authors or other persons. Self-application closes the framework. Continuum models, discrete models, cellular automata, XOR-based constructions, effective theories, quantum representations, and Kunato itself receive no exemption from the admission rules. Failure to identify a continuum ontology does not identify a discrete ontology, empirical adequacy of a constructive model does not establish its fundamental realization, and formal validity of Kunato does not confer physical ontological status on Kunato. The framework therefore entails neither a privileged fundamental model nor ontological nihilism. Not identified does not imply false, and not admitted does not imply nonexistent. Kunato Core Ver.5.0.0 provides a unified formal and computational vocabulary for ontological admission, finite-data non-identification, finite-record discrimination, inverse problems, coarse-graining, property factorization, representation refinement, effective dynamics, statistical invariants, temporal inference, information-theoretic interpretation, criticality assessment, model-class identification, provenance, epistemic-state revision, and scientific realism. Its objective is not to determine a preferred ontology by methodological fiat, but to make the inferential boundaries between representation, observation, identification, and physical realization explicit and auditable. The framework is summarized by four constraints: no hidden epistemic transition; no hidden ontological promotion; no untyped representational transport; and no self-exemption. Its terminal methodological principle is: no representation receives automatic ontological privilege.
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.
Epistemic Physics: Scope, Boundaries, and Structural Commitments (Version 2.0) This article develops a formally delimited account of “Epistemic Physics” as a structural research program situated at the intersection of quantum foundations, relational approaches, information-theoretic reconstruction, and scientific machine learning. The term is not introduced as a new metaphysical doctrine, but as a rigorously constrained framework in which epistemic commitments are considered operative only when they modify admissible state spaces, transformation rules, or stability structures of physical description. The paper proceeds in three stages. First, it reconstructs the historical trajectories through which epistemic considerations became structurally relevant in modern physics. Second, it formalizes Epistemic Measurement Dynamics (EMD) within C*-algebraic quantum theory, introducing sensitivity metrics, spectral stability constraints, completely positive trace-preserving (CPTP) contractivity, and a bounded-sensitivity theorem under weak-* compactness. Third, it clarifies the relationship of this structural layer to ontological-model no-go theorems, including the Pusey–Barrett–Rudolph result, and to QBist approaches, establishing domain separation rather than refutation. The deposit includes two canonical publication-rendered PDF variants and the full canonical release archive (ZIP). Canonical Release SHA256: 1CD95CEDCF03EBFA77B7C5074F7C2B281A73FE77F31CB3F1D1BA6266521850EB This SHA256 corresponds to: EpistemicPhysics_v2_0_RELEASE.zip Any modification of the archive will alter the hash. Integrity may be independently verified using SHA256. Date: 2026-02-27
This paper presents a continuous structural ontology in which quantum mechanics, field theory, and general relativity are interpreted as regime-specific descriptions of a shared underlying system. Rather than introducing new forces or modifying established equations, the framework identifies three minimal and persistent structural elements across physical regimes: admissible configuration space, propagating constraint, and geometry as the macroscopic record of accumulated interaction. The work is intentionally interpretive rather than revisionary. It proposes that physical evolution can be understood as the propagation of constraint over admissible configurations, with increasing restriction giving rise to stable structure, classical behavior, and geometric curvature. Established mathematical formalisms—including Hilbert space, field equations, and general relativity—are preserved and reinterpreted within a common structural language. This framework aims to improve conceptual continuity across quantum, field, and geometric domains while remaining fully consistent with existing empirical results. It does not claim a complete formal unification, but instead offers a minimal ontological foundation that may clarify relationships between currently distinct theoretical descriptions. This paper forms part of the broader Communication Matrix research program.