B4 Root Systems Absent in Video Results; D4 Square Lattice Anchor Found — E8 Intelligence Research
Year: 2026
Type: preprint
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
Author: Caldin, Andrew Stewart
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7210278337
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