teal-sea/zeta-lab
Let N(T,2T) count the nontrivial zeros of the Riemann zeta function with ordinate in (T,2T], with multiplicity, and N_0^s(T,2T) the simple zeros among them on the critical line. The Lean development accompanying arXiv:2608.13637 (anthropics/zeta-23-lean) proves, for Mathlib's riemannZeta and unconditionally, that for every eps > 0 and all large T, (H - eps) N(T,2T) = 2, c > 0, m >= n, p > 0 with c(m-(n-1)) 0 and all large T, (Phi_n(n,c,m,p) - eps) N(T,2T) <= N_0^s(T,2T), where Phi_n(n,c,m,p) = (H - (n-1)(m-1)/(pm)) / (1 - c(m-(n-1))/m). At n = 7 this is Ainta's theorem. THE THREE-POINT…
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