Riemann Hypothesis: No New Proof, Only Expository and Sufficient-Condition Approaches — E8 Intelligence Research

FINDING: No new proof or disproof of the Riemann hypothesis emerges; the sources are expository (Tao, 3Blue1Brown) plus one arithmetical approach paper (arXiv:0906.4155v7) that gives a sufficient condition via the Liouville function partial sums. | MATH: Riemann zeta function ζ(s) = Σ n⁻ˢ (Re(s)>1), analytic continuation to ℂ\{1}; nontrivial zeros conjectured at Re(s)=1/2. Sufficient condition (from arXiv paper): RH holds if the partial sum L(x) = Σn≤x λ(n) satisfies L(x) = O(x1/2+ε) for all ε>0, where λ(n) is the Liouville function (λ(n)=(-1)^Ω(n), Ω = total prime factors). The paper also derives a formula for L(x) involving a sum over zeros of ζ, linking the partial sums to the zero distribution. | CONNECTION: The critical line Re(s)=1/2 is the exact midpoint of the critical strip 0 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com