USAC: Unified Spectral Alignment & Coherence Framework – A New Mathematical Paradigm for Prime Gaps, Dark Energy, Neural Dynamics, and Spacetime Geometry

Source abstract

This work introduces the Unified Spectral Alignment & Coherence Framework (USAC), a new mathematical framework that uncovers deep connections between prime gaps, dark energy, neural dynamics, and spacetime geometry. At the heart of this framework lies a simple yet powerful idea: the zeros of the Riemann zeta function naturally align with one another based on frequency harmony. This Natural Alignment Principle requires no external regulation and emerges purely from the intrinsic structure of the spectral modes.The framework provides a unified mathematical language for describing how spectral modes interact, synchronize, and cohere across different scales. It introduces key concepts such as spectral alignment, alignment dynamics, and spectral coherence, which together form a coherent picture of how order and structure emerge in complex systems. Unlike classical approaches that treat spectral modes as independent, USAC reveals a hidden layer of organization governed by natural alignment.The framework is applied to four fundamental domains: prime gaps, dark energy, neural dynamics, and spacetime geometry. For prime gaps, USAC predicts the statistical distribution through alignment dynamics. For dark energy, the coherence term models cosmic acceleration. For neural dynamics, alignment describes synchronization patterns in the brain. For spacetime geometry, the framework induces a spectral metric that connects quantum mechanics with general relativity.Numerical simulations using the first 100 non-trivial zeta zeros confirm that the system converges to a unique stable state, validating the theoretical predictions. The results demonstrate that alignment and coherence are not only mathematically rigorous but also computationally observable.Beyond its mathematical depth, USAC offers a fresh perspective on some of the most profound questions in modern science. It bridges number theory, cosmology, neuroscience, and fundamental physics, suggesting that the same principles of alignment and coherence may underlie the distribution of primes, the expansion of the universe, the synchronization of neural activity, and the geometry of spacetime.This work establishes a new paradigm in spectral theory and mathematical physics, opening doors to interdisciplinary research and practical applications. The framework is not merely a collection of equations; it is a vision of how the universe organizes itself through natural harmony.