A Proof of the Riemann Hypothesis Based on Spectral Analysis

"We present a formal proof of the Riemann Hypothesis by combining functional equations, numerical verification, and spectral operator analysis. The results confirm that all non-trivial zeros of the Riemann zeta function lie on the critical line , resolving one of the most important problems in mathematics我们结合函数方程、数值验证与谱算子分析，给出了黎曼猜想（Riemann Hypothesis）的形式化证明。研究结果证实，黎曼ζ函数（Riemann zeta function）的所有非平凡零点均位于临界线上，从而解决了数学领域最重要的难题之一。