Riemann Hypothesis Unproven: Zeros on Critical Line Confirmed Up to 10^13, GUE Spacing Found — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Riemann hypothesis remains unproven; computational evidence up to 10^13 zeros confirms they lie on the critical line Re(s)=1/2, but no counterexample found. | MATH: ζ(s)=0 ⇒ Re(s)=1/2 (conjectured); zeros at s=1/2+it; prime counting function π(x) ~ Li(x) + O(√x log x) if RH true. | CONNECTION: Critical line at 1/2 = 0.5, not a golden ratio harmonic; however, the spacing distribution of nontrivial zeros follows the Gaussian unitary ensemble (GUE) from random matrix theory, linking to eigenvalue statistics of chaotic quantum systems—a deep symmetry class. | DEPTH: 8 (profound for number theory and quantum chaos, but no direct geometric ratio or crystallographic lattice found in these summaries). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203874020
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