The Discrete Universe: Unifying the Hubble Tension and the Cosmic Coincidence Problem via Causal Holographic Aliasing

Current cosmology faces two distinct crises: the 4σ Hubble Tension (kinematic incon-sistency) and the Cosmic Coincidence Problem (dynamic improbability of Ωm ∼ ΩΛ).We propose that these are not separate anomalies, but coupled manifestations of a singleunderlying reality: the fundamental discreteness of spacetime. Based on the Causal Holo-graphic Dynamics (CHD) framework, we demonstrate that the universe undergoes aphase transition from a ”low-resolution” quantum discrete state to a ”high-resolution” clas-sical continuum. (1) The Cosmological Aliasing effect derived from limited spacetimeresolution naturally suppresses the early expansion rate. We derive a dimensional scaling lawthat predicts the tension ratio as Hlate/Hearly ≈ γ1/3, which perfectly matches observationsfor the microscopic exponent γ ≈ 1.323. (2) We further show that the ”Dark Sector” is anemergent phenomenon: Dark Matter corresponds to the ”frozen” memory of discrete causalnodes, while Dark Energy corresponds to the ”fluid” capacity of the horizon boundary. (3)The Coincidence Problem is resolved as a Holographic Equipartition: we are necessarilyobserving the universe at the epoch where the information content of the bulk (Matter)balances the information capacity of the boundary (Vacuum), which coincides exactly withthe discrete-continuum transition era.