Atomic Phase Resonance (APR) Theory and the Cosmic Unification Equation: A Multiscale Empirical and Numerical Synthesis

This paper presents the Atomic Phase Resonance (APR) Theory and its governing Cosmic Unification Equation, developed to resolve the fundamental crises of particle-based Dark Matter (Lambda-CDM) models across local, intermediate, and cosmological scales. By reformulating gravitational anomalies as non-linear phase-locking interactions between the vacuum phase field and baryonic matter, the APR framework eliminates the need for hypothetical dark matter particles. We present rigorous mathematical formulations and empirical validation across 175 SPARC galaxy rotation curves (mean absolute error of 6.14 km/s), galaxy cluster gravitational lensing (5-7x mass potential amplification), and the Planck Cosmic Microwave Background (CMB) acoustic peak spectrum (ell = 2 - 2500) with a mean deviation of 1.45%.