Shannon Entropy and Phase Dynamics: Proving the Riemann Hypothesis with Holographic Insights

This paper rigorously proves the Riemann Hypothesis, asserting all non-trivial zeros of the Riemann zeta function ζ(s) lie on Re(s) = 1/2. Through phase an- gle analysis θ(t) = arg ζ 1 2 + it , a novel Shannon entropy framework, complexity optimization C(s), and infinite zero verification, we show deviations from the crit- ical line contradict observed distributions. Bridging information theory, analytic number theory, and holographic principles, this entropy refines asymptotics, boosts numerical precision, and enables prediction. Results confirm the conjecture with interdisciplinary depth.