Spectral Operator Approach to the Riemann Hypothesis: Non-Hermitian Eigenvalues and the Critical Line — E8 Intelligence Research

FINDING: The Riemann Hypothesis (RH) remains unproven; computational evidence is extensive but non-exhaustive. A notable theoretical strategy links RH to eigenfunctions of a non-Hermitian operator, suggesting a spectral interpretation of the zeta zeros. | MATH: Riemann zeta function ζ(s) = Σ n⁻ˢ (Re(s)>1), analytically continued. RH: all non-trivial zeros satisfy Re(s) = 1/2 (critical line). The operator D⁺ (non-Hermitian) has eigenvalues = zeros of ζ(s); RH ⇔ orthogonality condition for its eigenfunctions. No closed-form ratio or new constant emerges from the cited sources. | CONNECTION: The critical line Re(s)=1/2 is a symmetry axis — a reflection symmetry in the complex plane. The spectral interpretation (Hilbert–Pólya) hints at a hidden self-adjoint operator, whose eigenvalues would be real (1/2 + iγ), implying a unitary symmetry — but no explicit geometric ratio (0.382, 0.618, etc.) or crystallographic group is directly evidenced. The base-60 connection is absent. | DEPTH: 8 — The

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com