Bottleneck Reduction and Proof of the Riemann Hypothesis via Operator-Algebraic Trace Rigidity

This work presents a rigorous operator-algebraic approach to the Riemann Hypothesis (RH). By interpreting the nontrivial zeros of the Riemann zeta function as the spectrum of a self-adjoint operator associated with a canonical, positive, scaling-invariant, Fourier self-dual trace on the ad`ele class space, the paper proves RH through trace rigidity, KMS state uniqueness, and type III$_1$ factor analysis. Convergence of all relevant Laplace and Fourier integrals is established to ensure a fully rigorous distributional framework.