Riemann Hypothesis: Unresolved, Arithmetical and Physical Approaches — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Riemann hypothesis remains unsolved; current research focuses on arithmetical approaches (Liouville partial sums) and speculative physical analogs (black holes), with no new proof or breakthrough. | MATH: Sufficient condition for RH: if \( \sum_{n \le x} \lambda(n) = O(x^{1/2+\epsilon}) \) for all \( \epsilon > 0 \), then all nontrivial zeros lie on \( \Re(s) = 1/2 \). (Liouville function \( \lambda(n) = (-1)^{\Omega(n)} \)). | CONNECTION: None found — no ratios (0.382, 0.618, 0.786, 1.618, 2.618), no base-60, no crystallographic symmetry in the provided sources. The black-hole link is qualitative (chaos/spectral statistics), not geometric-harmonic. | DEPTH: 2 — the arxiv paper (0906.4155v7) is a known partial approach, but the videos are expository; no new equations or constants emerge. The RH itself is profound (depth 10), but these findings add no new mathematical structure. 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: W7212370811
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