No Primary Sources on Ramanujan Zeta Zeros at Re(s)=6 or Hardy Conjecture — E8 Intelligence Research

FINDING: Search returned no primary-source result on "Ramanujan zeta zeros at Re(s)=6" or a "Hardy conjecture" in that form; the corpus is dominated by expository Riemann-zeta material plus one unrelated particle-physics paper. | MATH: Riemann zeta ζ(s)=Σ n⁻ᵉˢ = Π_p (1−p⁻ˢ)⁻¹, analytic continuation to ℂ\{1}, functional equation ξ(s)=ξ(1−s) with ξ(s)=½s(s−1)π⁻ˢ/²Γ(s/2)ζ(s); nontrivial zeros conjectured on Re(s)=½; Montgomery pair-correlation R₂(x)=1−(sin πx/πx)²; CKM angle γ from B±→D(→K⁰_S h′⁺h′⁻)h± (arXiv:2604.05701). | CONNECTION: The Montgomery form 1−(sin πx/πx)² is the GUE (β=2) eigenvalue-repulsion kernel — a random-matrix / root-system symmetry class (Dyson's threefold way: β=1 orthogonal, β=2 unitary, β=4 symplectic). This is the only genuine geometric-harmony link present: spectral rigidity of a determinantal point process, not a φ-ratio. No 0.382/0.618/0.786/1.618/2.618, no base-60, no crystallographic lattice appears in the supplied evidence. | DEPTH: 3 Precise notes on the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23690715
Primary Topic
Analytic Number Theory Research
Type
preprint
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No Primary Sources on Ramanujan Zeta Zeros at Re(s)=6 or Hardy Conjecture — E8 Intelligence Research

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

No Primary Sources on Ramanujan Zeta Zeros at Re(s)=6 or Hardy Conjecture — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned no primary-source result on "Ramanujan zeta zeros at Re(s)=6" or a "Hardy conjecture" in that form; the corpus is dominated by expository Riemann-zeta material plus one unrelated particle-physics paper. | MATH: Riemann zeta ζ(s)=Σ n⁻ᵉˢ = Π_p (1−p⁻ˢ)⁻¹, analytic continuation to ℂ\{1}, functional equation ξ(s)=ξ(1−s) with ξ(s)=½s(s−1)π⁻ˢ/²Γ(s/2)ζ(s); nontrivial zeros conjectured on Re(s)=½; Montgomery pair-correlation R₂(x)=1−(sin πx/πx)²; CKM angle γ from B±→D(→K⁰_S h′⁺h′⁻)h± (arXiv:2604.05701). | CONNECTION: The Montgomery form 1−(sin πx/πx)² is the GUE (β=2) eigenvalue-repulsion kernel — a random-matrix / root-system symmetry class (Dyson's threefold way: β=1 orthogonal, β=2 unitary, β=4 symplectic). This is the only genuine geometric-harmony link present: spectral rigidity of a determinantal point process, not a φ-ratio. No 0.382/0.618/0.786/1.618/2.618, no base-60, no crystallographic lattice appears in the supplied evidence. | DEPTH: 3 Precise notes on the 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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