Computable Wavefunction Realism (CWFR) is an ontological framework for quantum theory derived from the semantic commitments of explanatory realism. Explanatory realism requires that physical magnitudes denote under admissible representations and that lawful evolution be closed on the intended ontic domain. Read literally, continuum ontology challenges these requirements through three distinct forms of semantic instability: domain instability arising from unbounded aggregation of fine-scale structure, range instability arising from non-open predicate structure, and closure failure under lawful evolution. CWFR does not begin by postulating computability or finite information; both arise as consequences of the semantic conditions required for physically meaningful ontology. The resulting answer is given by four postulates: Lorentz-invariant spectral band-limitation, identification of the ontic domain with states admitting Type-2 computable names under the chosen representation, admissible successor dynamics given by total Type-2 computable maps on the admissible domain, and restriction of physically meaningful predicates to those whose truth sets are open in the representation topology. The paper develops the structural consequences of these constraints and establishes non-vacuity through explicit admissible successor constructions. CWFR is not proposed as a replacement for continuum quantum mechanics at the level of mathematical formalism, but as a restriction on ontological interpretation imposed by semantic stability conditions. Macroscopic structure arises from refinement geometry induced by admissible stability predicates, classical worlds emerge as maximal refinement threads, and probability assignments operate on locally finite refinement partitions. Extension to realistic interacting quantum field theories is identified as a programmatic direction rather than a completed result.
Computable Wavefunction Realism (CWFR) is an ontological framework for quantum theory derived from the semantic commitments of explanatory realism. Explanatory realism requires that physical magnitudes denote under admissible representations and that lawful evolution be closed on the intended ontic domain. Read literally, continuum ontology challenges these requirements through three distinct forms of semantic instability: domain instability arising from unbounded aggregation of fine-scale structure, range instability arising from non-open predicate structure, and closure failure under lawful evolution. CWFR does not begin by postulating computability or finite information; both arise as consequences of the semantic conditions required for physically meaningful ontology. The resulting answer is given by four postulates: Lorentz-invariant spectral band-limitation, identification of the ontic domain with states admitting Type-2 computable names under the chosen representation, admissible successor dynamics given by total Type-2 computable maps on the admissible domain, and restriction of physically meaningful predicates to those whose truth sets are open in the representation topology. The paper develops the structural consequences of these constraints and establishes non-vacuity through explicit admissible successor constructions. CWFR is not proposed as a replacement for continuum quantum mechanics at the level of mathematical formalism, but as a restriction on ontological interpretation imposed by semantic stability conditions. Macroscopic structure arises from refinement geometry induced by admissible stability predicates, classical worlds emerge as maximal refinement threads, and probability assignments operate on locally finite refinement partitions. Extension to realistic interacting quantum field theories is identified as a programmatic direction rather than a completed result.
Computable Wavefunction Realism (CWFR) is a finite-information ontology for quantum mechanics that preserves Everettian explanatory structure while rejecting continuum wavefunction realism as fundamental ontology. The motivation is semantic. Under explanatory realism, physical magnitudes must denote under an admissible semantics, and dynamics must be semantically closed on their ontic domain. Continuum ontology exhibits two independent instabilities. On the domain side, unbounded fine-scale structure permits lawful dynamics to force dependence on unbounded collections of independent contingencies, producing non-denoting magnitudes and loss of semantic closure. On the range side, continuum ontology admits distinctions among real-valued magnitudes that no bounded-input-dependent interface can stably track. In particular, computability is not a physically meaningful predicate at fixed finite resolution, since computable and noncomputable reals are both dense. Such distinctions are semantically inert as ontology. CWFR enforces the required stability conditions via three postulates: (I) a Lorentz-invariant spectral band-limit bounding independent fine-scale degrees of freedom; (II) amplitudes restricted to Type-2 computable complex numbers, aligning the range of magnitudes with admissible semantics; and (III) evolution by finitely specified, oracle-free successor maps that are total on the resulting configuration space. Within this finite-information setting, decoherence yields finite packet partitions and finitely branching successor structure, with Born weights defined over finite packet partitions, while the continuum Hilbert-space formalism survives only as semantic scaffolding for symmetry and approximation. Full constructions and proofs appear in the CWFR manuscript and companion papers.
Configuration Realism (CR) is a physical ontology consisting of a finite, timeless configuration space. Each configuration is a complete arrangement of fundamental degrees of freedom; none evolves; phase attaches additively to degrees of freedom and is defined relationally, relative to a stage of an observer chain. Information exists only as finite, lossy physical records. Each record defines a compatibility class, the configurations it cannot distinguish, and probability is defined as counting over these classes. The framework's derived core is proved and computed in three companion papers under named structural assumptions. The population of an outcome class equals N|α|²: the Born rule as a theorem, with the frequency reading consuming exactly one typicality principle. The CHSH quantity assembled from integer counts reaches 2√2 to O(1/N), the ontology giving up counterfactual definiteness in the plain Bell scenario—and the absoluteness of outcomes where Wigner's-friend extensions demand it—rather than locality or free settings. And equipped with a local move set, counted populations propagate as wavepackets: the effective mass is the inverse hopping rate of elementary refinement, the potential is a cell-dependent phase cost, and the counted dynamics reproduces Schrödinger phenomenology with the number of configurations conserved exactly at every stage. Around this core, closure laws order records by refinement. Observers are chains of record-bearing stages; change is difference read along a refinement chain; time is the emergent coordinate that labels it; and closure distance, accumulating in discrete quanta, measures the restructuring refinement requires. Direct consequences follow for entropy and the arrow of time, for the classical limit, and for objectivity as redundancy. The remainder is a labeled research program: causal structure, Lorentzian geometry, geodesic dynamics, and horizon thermodynamics as conjectured continuum limits of closure geometry, with the constructions that would establish them stated as open problems. A dedicated section collects the framework's distinctive predictions—the O(1/N) family separating a counting world from continuum quantum mechanics—each with its mechanism and in-principle test. Every claim in the paper is tabulated with its status: postulate, theorem, verified, argument, conjecture, or open.
The ontology of quantum theory remains contested. Particle ontology struggles with the non-classical behavior of quantum entities, while wavefunction realism appears to locate the fundamental ontology in a high-dimensional mathematical state space rather than in ordinary physical space. Quantum field theory further complicates particle ontology by treating particle number as representation-dependent and, in interacting theories, often only emergent or approximate. This paper develops a philosophy-facing account of Geometric Monism (GM), a continuous-geometric ontology in which quantum entities are modeled as finite torsional standing-wave structures in a 5-dimensionalm geometric manifold governed by a universal Planck Stiffness κT = c4/G.The aim is not to replace the predictive formalism of quantum mechanics or quantum field theory. Rather, the paper asks whether the entities represented by those formalisms may be interpreted as continuous geometric structures rather than point particles, abstract wavefunctions, or merely emergent field excitations. GM distinguishes between continuous entity ontology and localized interaction events. To resolve the scale mismatch between the fundamental geometric stiffness and empirical observables, GM proposes a tripartite ontology: a Planck-scale topological core, a dimensional matching transition layer, and a macroscopic exterior dressing field. Observed measurement outcomes arise through boundary-conditioned interactions with this macroscopic dressing in accessible 4-dimensional spacetime.The paper presents the core ontological commitments of GM, including the active but observationally constrained embedding coordinate, the tripartite scale ontology, and the exact 40-degree operational microscopic sector obtained by imposing the Anti-Axial Constraint on the 5-dimensional torsion tensor. These commitments are compared with point-particle ontology, wavefunction realism, Bohmian mechanics, Everettian interpretations, and structural realism. The result is a proposed continuous-geometric primitive ontology: quantum objects are real, multi-scale geometric entities, while probabilities and measurement outcomes arise from localized boundary access to their macroscopic field extensions. Furthermore, the paper outlines the rigorous mathematical stability proofs required to validate such continuous ontologies.
Continuum physics represents states as real- or complex-valued fields and dynamics as operators on infinite-dimensional function spaces. Under an ontic interpretation, however, fundamental evolution must be semantically total: it must take every admissible state specification to a successor state specification in which all admitted magnitudes remain denoting. We make this requirement explicit using standard admissible representations, in which denotation is characterized by bounded finite-precision input dependence on state descriptions. We show that standard continuum dynamics can violate this semantic closure requirement even when the underlying PDE is linear, well posed, and uniquely solvable. The obstruction is forced extensional totalization: a regional readout can require joint control over countably many individually well-behaved contributions in a way that destroys bounded input dependence and hence denotation. Because locality commits a field ontology to treating spatial restrictions on compact regions as single physical magnitudes, this failure mode cannot be avoided by appealing to pointwise readouts or sequential access. Reanalyzed in these terms, the Pour-El and Richards Theorem 2 construction for the three-dimensional wave equation provides a concrete witness: admissible finite-energy initial data evolve to states whose regional field restrictions do not admit admissible names in the required function-space topology. The obstruction is semantic rather than epistemic: it does not concern what can be computed or observed, but the failure of continuum evolution to preserve denotation under realist locality commitments. The conclusion is eliminative: unrestricted continuum field ontology cannot serve as the basis of a semantically closed fundamental dynamics.
Continuum physical theories model states as real- or complex-valued fields and dynamics as linear operators on infinite dimensional spaces. Under explanatory realism, an ontic interpretation incurs two semantic commitments: (i) real-valued physical magnitudes must denote relative to the theory’s admissible state interface, and (ii) the theory must be semantically closed under its own evolution and readout rules. Denotation is interface-relative: it requires the existence of a total continuous witness on names. Equivalently, it requires bounded input dependence at each fixed finite precision. Failure of bounded input dependence is captured by forced extensional totalization (FET), in which even coarse output precision cannot be stabilized by any finite prefix of a state name. We give a physics-facing construction of FET for the three-dimensional wave equation with Kirchhoff point readout. We construct a countable family of smooth, compactly supported, finite-energy initial states localized on pairwise disjoint shrinking latitude belts on the Huygens sphere, and restrict the admissible domain to states containing at most one localized contingency. Each nonzero belt perturbation is normalized to contribute the same order-one amount to the readout, while the zero state contributes none. Under any non oracular state interface satisfying a minimal locality-of-access condition, no finite prefix can rule out activation of some sufficiently deep belt. The induced point readout therefore behaves like the existential predicate "some belt is active'', exhibits FET at the zero state, and fails to denote. Semantic closure fails: the evolution-readout pipeline yields a localized point magnitude that is non-denoting relative to the fixed state interface. The result isolates a semantic obstruction to ontic readings of continuum dynamics. It is independent of computability, predictability, or measurement feasibility, and it holds despite smooth compact support, finite energy, and classical well-posedness.
Many familiar quantum puzzles may begin not with what the quantum object is taken to be, but with what we demand of its representations. This paper develops a representability framework in which an admissible representation may be subjected to an additional representational requirement whose admissibility must then be tested. When that stronger demand cannot be satisfied while preserving the relations the representation is required to maintain, a representability obstruction arises. Spectral incompatibility, entanglement, interference, and Bell-violating correlations are examined through this common methodological pattern. Their mathematical structures remain distinct; what they share is the question of whether an already admissible representation can satisfy the additional representational requirement being imposed. The framework also separates representability obstruction from outcome-conditioned refinement, the operation on the represented state conventionally described as “wavefunction collapse.” Given an already admissible spectral structure and a recorded outcome, the represented state undergoes outcome-conditioned refinement: the corresponding spectral alternative is selected and the state is refined relative to it. This operation is defined at the Hilbert-space and spectral level before any coordinate wavefunction is introduced. A coordinate wavefunction expresses the refined state only after a coordinate representation has been chosen. The framework therefore treats recorded outcomes as empirical givens and does not attempt to explain why one particular outcome rather than another is physically produced. At the structural level, the framework is organized by the symmetry group, the observable algebra, and the symmetry action. Their Hilbert-space realization supplies the spectral and symmetry-compatible representational structures within which admissibility and invariant comparison are formulated. Within this setting, the Born weight is treated as an invariant quadratic comparison between the represented state and a spectral alternative and is not, by itself, identified with ignorance over pre-existing jointly defined values. An individual Born measure therefore does not by itself supply the joint classical representation required by classical ignorance. The resulting picture places structure before wave description, distinguishes representational impossibility from conditional refinement, and isolates precisely where stronger representational demands cease to be admissible. This is version 1.0 of the manuscript.