Non-Hermitian Operator Framework Links Riemann Zeros to Eigenfunctions — E8 Intelligence Research

FINDING: Riemann Hypothesis remains unproven; computational evidence supports all nontrivial zeros on critical line Re(s)=1/2, with a proposed non-Hermitian operator framework linking zeros to eigenfunctions. | MATH: ζ(s)=∑ₙ₌₁^∞ n⁻ˢ (Re(s)>1); analytic continuation to ℂ\{1}; functional equation ζ(s)=2^s πˢ⁻¹ sin(πs/2) Γ(1−s) ζ(1−s); critical line s=1/2+it; zeros ρ_n satisfy ζ(ρ_n)=0, Re(ρ_n)=1/2 (conjectured); proposed operator D^† with eigenvalues = zeros, orthogonality condition ⟨ψ_m|D^†|ψ_n⟩=0 for m≠n. | CONNECTION: The critical line Re(s)=1/2 is the fixed point of the functional equation symmetry s↔1−s — a reflection symmetry about the point 1/2, which is the arithmetic mean of 0 and 1, and the geometric midpoint of the critical strip. This 1/2 is the same ratio as the half-turn in crystallographic 2-fold symmetry (rotation by π), and the critical line's invariance under s→1−s mirrors the self-duality of the golden ratio's inverse (0.618 = 1/1.618) in that both are fixed p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com