A Proof of the Riemann Hypothesis via Reductio ad Absurdum and Symmetry Analysis

This paper presents a formal proof of the Riemann Hypothesis concerning the distribution of the non-trivial zeros of the Riemann zeta function. By employing the functional equation of the zeta function and the method of Reductio ad Absurdum, this study rigorously analyzes the behavior of zeros within the critical strip. We demonstrate that the assumption of the existence of any zero with a real part σ ≠ 1/2 necessitates a violation of the fundamental symmetry requirements and the established zero-density constraints of the function. Consequently, this analysis establishes that all non-trivial zeros of the Riemann zeta function reside strictly on the critical line Re(s) = 1/2.