Computable Wavefunction Realism: A Finite-Information Ontology

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.