The Coherence Evolution Model

This paper introduces the Coherence Evolution Model (CEM), a novel framework positing that prime numbers and their arithmetic correlations govern universal coherence across scales. Empirical validation of the CEM is presented through fractal analysis of the Cosmic Microwave Background (CMB), revealing a fractal dimension matching the golden ratio and excess power at prime-indexed multipoles. These findings challenge the standard inflationary paradigm. The paper addresses critiques, outlines falsifiable predictions across cosmology, biophysics, and materials science, and invites independent verification of this unifying paradigm. * Prime Basis: The paper proposes that physical systems occupy orthogonal states indexed by primes, minimizing entropic interference. This suggests a fundamental connection between prime numbers and the building blocks of reality. * Zeta-Regulated Dynamics: The Riemann zeta function, which is closely related to prime numbers, governs long-range order via arithmetic quantum chaos. * Empirical Validation through CMB Fractality: The paper claims that the fractal dimension of the Cosmic Microwave Background (CMB) is related to the golden ratio, which arises from entanglement entropy calculated based on the distribution of prime numbers. * Prime-Indexed Coherence and the Horizon Problem: The uniformity of the CMB across causally disconnected regions is explained by "prime-indexed coherence," where primes carry non-local correlations. * Excess Power at Prime Multipoles: The paper also claims to find excess power in the CMB's harmonic spectrum at multipole moments that correspond to prime numbers. * Prime-Energy Correspondence: The paper explores the relationship E_p = \log p, linking prime numbers to energy scales in physical systems. * Mathematical Necessity: Primes are linked to the zeros of the Riemann zeta function, and the von Mangoldt function, \Lambda(n) = \log p for n = p^k, encodes the density of primes. * Physical Justification: The logarithm converts multiplicative primes into additive energy scales, mirroring how entropy converts multiplicative microstate counts into additive quantities. * Holographic Scaling: Primes are posited to label Planck-scale "atoms" of spacetime, with their spacing in energy reflecting holographic discreteness. In essence, the paper proposes a model where prime numbers are not just mathematical abstractions but are fundamental to the structure and behavior of the universe at various scales.