The Computable Universe: A Single Axiom Deriving Dark Matter, Gravitational Discretization, and the Necessity of Quantum Gravity

We propose a single axiom, that physical law is constrained to computable operations, and derive five consequences spanning dark matter, gravitational physics, and quantum gravity. The axiom implies that electromagnetic interactions, which require algorithmic evaluation of field values, can only access a computable subset of spacetime, while gravity, operating through manifold geometry, couples to all matter regardless. This asymmetry produces the observed dark matter fraction as an information-theoretic discrepancy rather than missing particles. The same axiom predicts distance-dependent gravitational resolution degradation (not a uniform lattice), explains anomalous early galaxy brightness observed by JWST, and requires gravity to be quantized to prevent superluminal inference through geometric field correlations. We present thirteen falsifiable predictions distinguishing this framework from both particle dark matter and modified gravity theories.