Riemann Hypothesis Remains Unproven; Partial-Sum Approach Conditional — E8 Intelligence Research

FINDING: No new proof or disproof of the Riemann Hypothesis (RH) emerges; the search yields pedagogical expositions and one arithmetical partial-sum approach (Liouville function) that remains conditional and incomplete. | MATH: RH states all non-trivial zeros of ζ(s) satisfy Re(s)=1/2. The arithmetical paper (arXiv:0906.4155v7) gives a *sufficient* condition: if the partial sums of the Liouville function λ(n) satisfy Σn≤x λ(n) = O(x1/2+ε) for all ε>0, then RH holds. The paper also derives a formula "curiously related" to that condition, but no proof of the bound is given. No new constants, ratios, or exact equations beyond the standard ζ(s) = Σ n⁻ˢ (Re(s)>1) and its functional equation ζ(s)=2^s πˢ⁻¹ sin(πs/2) Γ(1−s) ζ(1−s). | CONNECTION: The critical line Re(s)=1/2 is a *geometric bisector* of the critical strip 0 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com