Prime Gap Instability and the Collapse of the Riemann Hypothesis

The Riemann Hypothesis (RH) asserts that all nontrivial zeros of the Riemann zeta function lie on the critical line ℜ(s) = 1/2 . In this paper, we prove that RH is false by demonstrating that the evolution of zeta zeros under the de Bruijn-Newman heat equation is fundamentally unstable. We establish that irregularities in prime gaps introduce an unbounded forcing term in the heat equation, leading to a necessary shift in the location of zeta zeros and forcing Λ > 0, contradicting RH. Furthermore, we resolve the Pair Correlation Conjecture independently of RH, showing that the statistical structure of zeta zeros remains unchanged under the heat evolution. This result confirms that the known statistical properties of the zeta function are not contingent on RH but instead arise from a deeper structural phenomenon tied to prime number modularity and diffusion dynamics. Our findings necessitate a fundamental reevaluation of the role of RH in analytic number theory, shifting focus toward a more geometrically and dynamically informed understanding of the zeta function's zeros.