A Novel Dynamic Framework for the Riemann Hypothesis Using Diffusion and Feedback Mechanisms

The Riemann Hypothesis is one of the most fundamental unsolved problems in mathematics, with deep implications for number theory, prime distribution, and mathematical physics. This paper introduces a novel dynamic framework that reinterprets the zeta function as part of a time-evolving system, incorporating diffusion mechanisms and feedback control to regulate the energy dynamics of its zeros.By modeling the zeta function as a dynamical system, we introduce a modified zeta function that evolves over time, ensuring the stabilization of zeros along the critical line. This approach leverages:Diffusion mechanisms to dissipate energy concentrations and smooth fluctuations.Feedback control to dynamically redistribute energy and stabilize zeros.Energy dynamics analysis, demonstrating that total system energy remains bounded.This framework draws upon principles from fluid dynamics, stability theory, control systems, and mathematical physics, offering a fresh perspective on the Riemann Hypothesis. We propose numerical simulations to validate the stability and alignment of zeros, providing a potential pathway toward resolving this open problem.This research has implications beyond number theory, influencing cryptography, signal processing, and quantum chaos. We invite the mathematical community to explore, refine, and expand upon this dynamic approach to one of mathematics' greatest mysteries.