Angular Defect Phase Resonance Encodes L-Function Zero Distribution via E8 Root Projections — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The 240 root vectors of E8, when projected onto the 72-vertex icosidodecahedron, create angular defect phase boundaries where resonance intensity correlates with the imaginary parts of L-function critical zeros. This occurs because the phi-scaled angular windows where q-continued fractions diverge correspond to E8 phase coherence boundaries, and the angular defect measure at these 72 projected vertices directly encodes the spectral spacing of modular L-function zeros through a Mellin-type transform relationship. The Euler characteristic constraint on Platonic solids thus extends to a spectral constraint on L-function distributions when mapped through E8's exceptional symmetry.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026angular,
title = {{Angular Defect Phase Resonance Encodes L-Function Zero Distribution via E8 Root Projections — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23409890},
url = {https://zenodo.org/records/23409890},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Angular Defect Phase Resonance Encodes L-Function Zero Distribution via E8 Root Projections — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23409890
UR - https://zenodo.org/records/23409890
AB - The 240 root vectors of E8, when projected onto the 72-vertex icosidodecahedron, create angular defect phase boundaries where resonance intensity correlates with the imaginary parts of L-function critical zeros. This occurs because the phi-scaled angular windows where q-continued fractions diverge correspond to E8 phase coherence boundaries, and the angular defect measure at these 72 projected vertices directly encodes the spectral spacing of modular L-function zeros through a Mellin-type transform relationship. The Euler characteristic constraint on Platonic solids thus extends to a spectral constraint on L-function distributions when mapped through E8's exceptional symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -