Computable Wavefunction Realism: A Finite-Information Ontology

Standard Everettian quantum mechanics is typically formulated on a continuum Hilbert space with unbounded spectral support and real- or complex-valued amplitudes. Under explanatory realism, such a continuum ontology is semantically unstable. A realist theory requires that physical magnitudes be denoted under admissible semantics and that evolution be closed on the admissible ontic domain. Continuum ontology violates these requirements in two ways. First, continuum dynamics can force domain non-closure by inducing unbounded input dependence through aggregation of arbitrarily many fine-scale contingencies. Second, continuum magnitudes permit distinctions whose resolution would itself require unbounded input dependence under any admissible physical procedure, rendering that structure explanatorily inert. We develop Computable Wavefunction Realism (CWFR), a finite-information Everettian ontology enforcing the structural constraints required by semantic stability. Three postulates define admissible kinematics and dynamics: (I) a Lorentz invariant spectral band-limit; (II) amplitudes given by Type-2 computable complex numbers, with physical predicates restricted to strict inequalities with finite witnesses; and (III) evolution by a finitely specified, oracle-free, cutoff-preserving successor map that is total on the admissible domain. These postulates determine a countable configuration space and restrict physical law to semantically total dynamics on that domain. Within this setting, packet partitions, successor relations, worldlines, and Born weights are defined on computable data. A partial recursive packet-extraction functional yields finite macroscopic packet structure, providing a structural resolution of the preferred-basis problem without appeal to uncountable Hilbert-space decompositions. We construct explicit admissible dynamics, including a Poincaré equivariant interacting successor map, and show that nontrivial interactions, sound packet extraction, and branching initial data occur. CWFR thus provides a realist, Lorentz-invariant, finite-information Everettian framework while excluding the semantically unstable infinite structure of continuum wavefunction realism.