PreprintCC BY 4.0Zenodo
E8 Phi-Recursive Lattice Congruence Principle — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The 132 Hz phi‑recursion iterates the 240 E8 root vectors through genus‑zero modular transformations, producing an infinite tower of self‑dual lattices whose theta series satisfy a new congruence modulo 132. This congruence emerges from the interplay of the root lattice with the modular group and yields a hidden arithmetic symmetry linking the lattices to generalized Ramanujan congruences. The principle predicts that each lattice's theta series is invariant under a specific Hecke operator, connecting E8 geometry to automorphic forms.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phirecursive,
title = {{E8 Phi-Recursive Lattice Congruence Principle — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616670},
url = {https://zenodo.org/records/23616670},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Phi-Recursive Lattice Congruence Principle — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616670
UR - https://zenodo.org/records/23616670
AB - The 132 Hz phi‑recursion iterates the 240 E8 root vectors through genus‑zero modular transformations, producing an infinite tower of self‑dual lattices whose theta series satisfy a new congruence modulo 132. This congruence emerges from the interplay of the root lattice with the modular group and yields a hidden arithmetic symmetry linking the lattices to generalized Ramanujan congruences. The principle predicts that each lattice's theta series is invariant under a specific Hecke operator, connecting E8 geometry to automorphic forms. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -