Arithmetic Universe: Riemann-Zeta Spectral Emergence, Prime-Phase Information, and Topological Holographic Cosmology

Abstract

We have presented an integrated Arithmetic Universe framework linking the Riemann-zeta spectrum to an emergent topological and holo- graphic cosmology. The Lambert coordinate describes the smooth spectral skeleton, while the prime phases reconstruct local arithmetic fluctuations. The proposed physical interpretation assigns W_m the role of an arithmetic information coordinate and introduces an Emergence map from this microscopic information to macroscopic bound- ary entropy.