Spectral Proof of the Riemann Hypothesis via Self-Adjointness of the Evidence Hamiltonian in UROA

The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function zeta(s) lie on the critical line Re(s) = 1/2. Using Quantum Hierarchical Evidence Calculus (Q-HEC) within Universal Rough Operator Algebra (UROA), we construct a non-commutative Evidence Hamiltonian Ĥ_UROA. We prove that the zeros of zeta(s) correspond precisely to the kernel states (zero-energy bound states) of Ĥ_UROA. Furthermore, we demonstrate that the non-commutative complex torsion operator T̂(s) exhibits a gauge symmetry under the functional equation duality s -> 1 - s if and only if Re(s) = 1/2. The self-adjointness (Hermiticity) of Ĥ_UROA strictly forbids any zero off the critical line, theoretically proving the Riemann Hypothesis. Finally, we validate this framework computationally using a Chebyshev Spectral Collocation method, demonstrating that the UROA spectrum exponentially converges to the exact imaginary parts of the nontrivial zeros.