"Finite-Step Operator Certificates for the Riemann Hypothesis"

Abstract We prove that all nontrivial zeros of the Riemann zeta function lie on the critical line. The argument rests on five analytic ingredients: (M1) explicit cut-offs yielding uniform nuclearity, (M2) self-adjointness of the perturbed dilation generator, (M3) non-vanishing of the global determi- nant with explicit lower bounds, (M4) a Grushin determinant–spectrum identity, and (M5) reality of the spectrum. Each item is proved with explicit constants, interval certificates, and archival code.