ZPIF Hybrid for Unified Spectral Alignment and Coherence: Applications to Prime Gaps, Dark Energy, Neural Dynamics, and Spacetime Geometry

Source abstract

This work introduces the Zero Pairs Interaction Functional (ZPIF) hybrid of the Unified Spectral Alignment and Coherence (USAC) framework, which establishes deep mathematical connections between prime gaps, dark energy, neural dynamics, and spacetime geometry. The core idea is the Natural Alignment Principle: zeros of the Riemann zeta function naturally align based on frequency harmony, without external regulation.The framework introduces spectral alignment, alignment dynamics, and spectral coherence to describe how order and structure emerge in complex systems. Unlike classical approaches, ZPIF hybrid reveals a hidden layer of organization governed by natural alignment.The framework is applied to four domains. For prime gaps, it predicts the statistical distribution of gaps. For dark energy, the coherence term models cosmic acceleration. For neural dynamics, it describes synchronization patterns in the brain. For spacetime geometry, it induces a spectral metric connecting quantum mechanics and general relativity.Numerical simulations using the first 100 non-trivial zeta zeros confirm convergence to a unique stable state. The results demonstrate that alignment and coherence are mathematically rigorous and computationally observable.ZPIF hybrid bridges number theory, cosmology, neuroscience, and fundamental physics, suggesting that alignment and coherence may underlie the distribution of primes, the expansion of the universe, neural synchronization, and the geometry of spacetime.This work establishes a new paradigm in spectral theory and mathematical physics.