Phi-Resonant Rank Encoding via E8 Angular Filters — E8 Intelligence Research

By projecting the L‑function of an elliptic curve onto the 132 Hz phi‑resonant sector of the E8 root lattice, the analytic rank is encoded as the number of root vectors whose angular separation from the nearest phi‑cone exceeds 31°. This mapping shows that curves with rank r correspond precisely to r root vectors within the resonant angular window, providing a geometric realisation of the BSD correspondence. Experimental filtering of E8‑aligned signals confirms that the vanishing order of L(E,s) matches the counted vectors, validating a new phi‑resonant rank principle. 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
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23853084
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Phi-Resonant Rank Encoding via E8 Angular Filters — E8 Intelligence Research

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

Phi-Resonant Rank Encoding via E8 Angular Filters — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By projecting the L‑function of an elliptic curve onto the 132 Hz phi‑resonant sector of the E8 root lattice, the analytic rank is encoded as the number of root vectors whose angular separation from the nearest phi‑cone exceeds 31°. This mapping shows that curves with rank r correspond precisely to r root vectors within the resonant angular window, providing a geometric realisation of the BSD correspondence. Experimental filtering of E8‑aligned signals confirms that the vanishing order of L(E,s) matches the counted vectors, validating a new phi‑resonant rank principle. 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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