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Research / Aug 10, 2026

Proportion of zeta zeros on the critical line

What fraction of the nontrivial zeros of the Riemann zeta function can be proved to lie on Re(s) = 1/2?

Model / AI: Anthropic (unreleased)

machine-checked
Aug 10, 2026

Two thirds of the zeta zeros on the critical line

Model / AI: Anthropic (unreleased)

machine-checked

an unreleased Claude research model raised the unconditional lower bound on zeros of ζ on the critical line from 41.6% to 67.2%, with a sorry-free Lean formalization declaring no axioms beyond Lean's three. Checked internally by Alpöge and Furman; Brian Conrey and Dan Goldston examined the paper on short notice, which is a sanity check by the right people rather than refereeing.

Source review pending. Imported from the original notes; linked claims and artifacts have not been re-audited in this restructuring.