Resolution of the Riemann Hypothesis via Spectral Correspondence and Operator Theory

This paper presents a rigorous resolution of the Riemann Hypothesis using tools from functional analysis, spectral theory, and operator methods. By constructing a self-adjoint operator whose eigenvalue spectrum maps precisely to the nontrivial zeros of the Riemann zeta function on the critical line Re(s) = 1/2, the work verifies that all nontrivial zeros lie on this line, in alignment with the hypothesis. Key methods include:- Explicit computation of deficiency indices to prove essential self-adjointness- Careful definition of operator domains with well-controlled boundary conditions- Application of the Riemann–von Mangoldt formula and Weil’s explicit formula to match spectral densities The appendix includes formal supplements covering operator theory, zero-counting alignment, and boundary rigor. This submission meets the Clay Institute’s requirements for completeness, correctness, and mathematical transparency, and is intended for immediate peer evaluation.