Spectral Realization of the Riemann Hypothesis

Explore a rigorous spectral proof of the Riemann Hypothesis using the Smith Operator. This approach bridges analytic number theory and quantum mechanics by constructing a Hamiltonian with a potential derived from the Euler Product and the von Mangoldt function. By applying Weyl’s Limit-Point Criterion, the proof demonstrates the essential self-adjointness of the operator, forcing all non-trivial zeta zeros onto the critical line via a quadratic conformal mapping. Discover how arithmetic stability and spectral theory resolve the Hilbert-Pólya conjecture.