Non-Hermitian Operator Links Riemann Zeros to Orthogonality Conditions — E8 Intelligence Research

FINDING: Riemann hypothesis remains unproven; computational evidence and a proposed non-Hermitian operator approach link zeros to orthogonality conditions. | MATH: Riemann zeta function ζ(s) defined by analytic continuation; zeros conjectured on critical line Re(s)=1/2. Proposed operator D^+ with eigenvalues equal to zeros; orthogonality condition for eigenfunctions. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60, crystallographic, or root system symmetries found in these sources. The non-Hermitian operator approach suggests a spectral interpretation but lacks direct geometric harmony. | DEPTH: 6 — The Riemann hypothesis is foundational to number theory and prime distribution, but these findings provide no new geometric or harmonic breakthroughs; the operator approach is speculative. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-17
DOI
https://doi.org/10.5281/zenodo.21973631
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Non-Hermitian Operator Links Riemann Zeros to Orthogonality Conditions — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Non-Hermitian Operator Links Riemann Zeros to Orthogonality Conditions — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Riemann hypothesis remains unproven; computational evidence and a proposed non-Hermitian operator approach link zeros to orthogonality conditions. | MATH: Riemann zeta function ζ(s) defined by analytic continuation; zeros conjectured on critical line Re(s)=1/2. Proposed operator D^+ with eigenvalues equal to zeros; orthogonality condition for eigenfunctions. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60, crystallographic, or root system symmetries found in these sources. The non-Hermitian operator approach suggests a spectral interpretation but lacks direct geometric harmony. | DEPTH: 6 — The Riemann hypothesis is foundational to number theory and prime distribution, but these findings provide no new geometric or harmonic breakthroughs; the operator approach is speculative. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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