Riemann Hypothesis: Verified Zeros, Unproven Proof, and Missing Geometric Harmony — E8 Intelligence Research

FINDING: Riemann Hypothesis remains unproven; computational verification extends to vast zero counts, and a proposed non-Hermitian operator framework links zeros to eigenfunctions, but no geometric-harmony ratio emerges from the provided sources. MATH: ζ(s) = Σ n⁻ˢ (Re(s)>1); analytic continuation to ℂ\{1}; critical line Re(s)=1/2; zeros ρₙ = 1/2 + iγₙ. Computational evidence: first 10¹³ zeros verified (Odlyzko–te Riele et al.), all on critical line. Proposed operator: D⁺ with eigenvalues = zeros, orthogonality condition ⟨ψₙ|ψₘ⟩ = δₙₘ for non-Hermitian D⁺ — no explicit equation given in abstract. No new constants or ratios reported. CONNECTION: None directly stated. However, the critical line Re(s)=1/2 is a symmetry axis — a reflection symmetry in the complex plane. The functional equation ζ(s) = 2ˢ πˢ⁻¹ sin(πs/2) Γ(1−s) ζ(1−s) exhibits s ↔ 1−s symmetry, which is a glide-reflection in the s-plane. This is a 2-fold symmetry, not a golden-ratio or base-60 structure. The "23% beyond" Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com