Resolutionism: the Universe as a Finite-Resolution Quantum Memory

Abstract

We prove in ZFC that every mathematical infinity is the Dedekind–MacNeille completion of a rank-finite generative system. The physical universe is such a system whose total information capacity is rigorously bounded by the covariant entropy bound and grows with the apparent-horizon area, reaching ≈10¹²² logical qubits today (Postulate 1). Together with dynamic register allocation via complementary recovery from a vacuum code subspace of effectively zero logical error rate (Postulate 2), this finite, slowly growing global memory forces objective collapse of macroscopic superpositions, bounds black-hole masses, explains dark energy and the Hubble tension, and derives all four laws of thermodynamics, all without free parameters. Nine sharp, parameter-free predictions follow, seven of which are laboratory-testable by 2045.

Keywords