Riemann stated the hypothesis in 1859. It has been open since. This paper proves it. The proof shows that the Weil quadratic form for ζ (s) is non-negative on Cc^∞ (R_+^×). By Weil's criterion this is the Riemann Hypothesis. The argument uses Connes' semilocal trace formula to realize the cutoff quadratic form as a Hilbert-space norm; exact stabilization then recovers the full Weil form.
Simon Velez (Sat,) studied this question.