Hypercubic Group BC₄ as Maximal Finite Subgroup of O(4) in Lattice QCD — E8 Intelligence Research

FINDING: The search results are largely tangential — dominated by pedagogical videos on Lorentz group representations and a lattice QCD paper on heavy-quark masses. No direct result addresses hypercubic lattice rotational symmetry as a discrete subgroup of the Lorentz group with finite-spacing artifacts. The closest mathematical anchor is the known fact that the hypercubic group \( \text{BC}_4 \) (order 384) is the maximal finite subgroup of \( O(4) \) relevant to lattice discretization. MATH: - Hypercubic rotational symmetry group: \( \text{BC}_4 \cong (\mathbb{Z}_2)^4 \rtimes S_4 \), order \( 2^4 \cdot 4! = 384 \). - Its rotation subgroup (proper): \( \text{SO}(4) \cap \text{BC}_4 \) has order 192. - Lorentz group \( O(3,1) \) has maximal compact subgroup \( O(3) \); discrete subgroups include the tetrahedral \( T_d \) (order 24), octahedral \( O_h \) (order 48), icosahedral \( I_h \) (order 120) — but these are 3D, not 4D. - In 4D Euclidean (Wick-rotated) space, the hypercu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com