Hypercubic B4 Root System: Absent from Search Results, Only 3D Thirring Models Found — E8 Intelligence Research

FINDING: The search results are a scattered set of educational videos and one arXiv paper on 3D lattice Thirring models; no direct mathematical derivation of hypercubic B4 root system or its gauge-theoretic representation is provided. The only substantive mathematical content is the arXiv abstract on 3D lattice fermion symmetries. | MATH: The arXiv paper (2201.01692v2) concerns Thirring models on 3D lattices — these are strongly interacting relativistic Fermi theories with four-fermion interactions. Key mathematical objects: lattice Dirac operator, fermion determinant, and the symmetry group of the cubic lattice (which for 3D is the octahedral group Oh, order 48). The paper discusses asymptotic safety (UV fixed point) and Dirac materials — the relevant symmetry is the discrete rotation group of the cubic lattice, which is a subgroup of O(3). No explicit equations, constants, or ratios are given in the abstract. The video titles mention "rotational symmetry of a cube" (Oh group, order 4 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com