A Primer on Computable Wavefunction Realism: A Finite-Information Ontology for Quantum Mechanics

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.