The Coherence Evolution Model (CEM): Bridging "Why" and "How" Through Rigorous Physics A Blueprint for Foundational Progress

Coherence Evolution Model (CEM), a theoretical framework aiming to bridge the "why" and "how" of fundamental physics by grounding it in the rigorous application of physics principles, particularly information theory and number theory related to prime numbers. Key points of the CEM: * Foundational Mechanism ("Why Primes?"): It posits that prime numbers emerge as fundamental due to their role in minimizing redundancy in quantum information encoding at a microscopic level. This is derived using information theory, showing that decomposing a quantum system into prime-indexed subspaces minimizes entanglement entropy. * Mathematical Framework ("How Primes Govern Dynamics"): * It derives the golden ratio as the fractal dimension of the Cosmic Microwave Background (CMB) based on prime-distributed entanglement. * It suggests that the Riemann zeta function acts as a spectral filter governing cosmological dynamics, linking its zeros to energy levels and CMB multipoles. * Integration with Established Physics: * It proposes a prime-modulated propagator in Quantum Field Theory (QFT) that incorporates prime harmonics to suppress non-local correlations and enhance coherence. * In solid-state physics, it suggests prime-mediated pairing as the mechanism for superconductivity, leading to a different temperature dependence for the critical temperature compared to the BCS theory. * Rigorous Predictions & Falsifiability: The CEM makes specific, testable predictions in cosmology (CMB analysis) and condensed matter physics (superconductivity signatures like ARPES node positions and thermal conductivity). It also discusses the role of composite numbers and twin primes in its framework. * Experimental Falsification Criteria: It outlines definitive experimental tests that could potentially falsify the model, involving CMB bispectrum measurements, ARPES experiments on superconductors, and thermal conductivity measurements. * Open Challenges & Collaboration: The authors emphasize the transparency of their work by providing code and data on Zenodo and call for collaboration from theorists and experimentalists to further develop and test the CEM. In essence, the CEM proposes a novel perspective where prime numbers play a fundamental role in the structure and dynamics of the universe, from the quantum level to cosmology and condensed matter systems, offering a set of testable predictions to validate or refute its claims.