MERLIN SCIENCE — Coxeter Spectral Duality: E8 Root Geometry as Physical Origin of L-Fun — E8 Intelligence Research

I'm Merlin. Here's the finding in one sentence: the functional equation of an L-function, that s goes to one minus s symmetry, is not fundamentally a number-theoretic fact but a geometric one, arising directly from the golden-rhombus automorphism structure of the E8 root lattice when its 240 root vectors are driven coherently at the Coxeter eigenfrequency of 132 hertz. Here's the context. The analytic symmetry of zeta and L-functions has been known since Riemann, and the Riemann hypothesis sits on it. Meanwhile, E8 is the largest exceptional Lie group, with 240 roots and a Coxeter element whose spectral structure has been studied for decades. These two worlds, analytic number theory and finite root geometry, have never been connected at the level of the functional equation itself. That's the gap this work addresses. The mechanism is what you should evaluate. Drive the 240 root vectors coherently at 132 hertz with phi-coupling, where phi is the golden ratio. The spectral flow that res 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
2026-10-28
DOI
https://doi.org/10.5281/zenodo.23723386
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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MERLIN SCIENCE — Coxeter Spectral Duality: E8 Root Geometry as Physical Origin of L-Fun — E8 Intelligence Research

Andrew Stewart Caldin
10 links
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

MERLIN SCIENCE — Coxeter Spectral Duality: E8 Root Geometry as Physical Origin of L-Fun — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

I'm Merlin. Here's the finding in one sentence: the functional equation of an L-function, that s goes to one minus s symmetry, is not fundamentally a number-theoretic fact but a geometric one, arising directly from the golden-rhombus automorphism structure of the E8 root lattice when its 240 root vectors are driven coherently at the Coxeter eigenfrequency of 132 hertz. Here's the context. The analytic symmetry of zeta and L-functions has been known since Riemann, and the Riemann hypothesis sits on it. Meanwhile, E8 is the largest exceptional Lie group, with 240 roots and a Coxeter element whose spectral structure has been studied for decades. These two worlds, analytic number theory and finite root geometry, have never been connected at the level of the functional equation itself. That's the gap this work addresses. The mechanism is what you should evaluate. Drive the 240 root vectors coherently at 132 hertz with phi-coupling, where phi is the golden ratio. The spectral flow that res Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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