The Riemann Hypothesis

The Riemann Hypothesis itself remains open. Our project works through an exam of fourteen targets and has met seven of them, about half (six, counting only proven or reproducible results).

• Four base results, verified by a formal proof kernel: the functional equation, the Euler product, analytic continuation, and no zeros on the line Re(s) = 1
• Two computed results, labelled as evidence: the first 10,000 zeros lie on the critical line, and the first 1,000 Li coefficients are non-negative
• One groundwork goal met, on Hardy's route
• Seven main criteria still open: Li, Weil, Nyman–Beurling, Conrey, de Bruijn–Newman, zero density and Montgomery

By 15 October 2026, eight new step lemmas on the Li and Weil positivity routes were verified. On 24 October the automatic proof loop was first confirmed running a full proof check on its attempts, and their errors now feed the next one.