B4 Root Systems Absent in Video Results; D4 Square Lattice Anchor Found — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-06
DOI
https://doi.org/10.5281/zenodo.22470334
Primary Topic
Quantum and Classical Electrodynamics
Type
preprint
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preprint

B4 Root Systems Absent in Video Results; D4 Square Lattice Anchor Found — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
preprint

B4 Root Systems Absent in Video Results; D4 Square Lattice Anchor Found — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The search results are dominated by lecture videos on spontaneous symmetry breaking (GHK mechanism), lattice gauge theory, and D4/hypergroup square-lattice analysis — but no direct mathematical content on B4 root systems or their lattice-gauge connections is extracted from these video titles/descriptions. The only concrete mathematical anchor is Wildberger's "Square Lattice via group D4 and its hypergroups," which explicitly treats the D4 (dihedral-4, order 8) symmetry of the square lattice and its hypergroup convolution structure. MATH: - D4 group: order 8, generated by rotation r (order 4) and reflection s (order 2), with relation srs = r⁻¹. Its irreducible representations: 4 one-dimensional (trivial, sign, two chiral) and 1 two-dimensional (standard rotation/reflection). - Hypergroup on D4: convolution algebra with structure constants satisfying associativity and a Haar-like measure; for the square lattice, the hypergroup is the double coset algebra of D4 acting on Z², Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quantum and Classical Electrodynamics
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B4 Root Systems Absent in Video Results; D4 Square Lattice Anchor Found — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS