A proof of the Riemann Hypothesis

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 C_c^∞(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.