Staggered Fermions Unify Lattice Chirality with B4 Root System and SO(8) Triality — E8 Intelligence Research

FINDING: Staggered fermions on hypercubic lattices realize a Z2^4 symmetry that maps directly onto the B4 root system and the SO(8) triality structure, unifying lattice chirality with exceptional Lie-algebraic topology. | MATH: The staggered fermion action on a d-dimensional hypercubic lattice reduces to 2^d degenerate "flavors" (here d=4 → 16 flavors). The discrete symmetry group is Z2^4 (translations by one lattice spacing in each of 4 directions). This Z2^4 is the Weyl group of the B4 root system (hyperoctahedral group, order 2^4·4! = 384). The 16 fermion components transform under the spinor representation of SO(8) — and SO(8) has triality: the vector (8_v), spinor (8_s), and conjugate spinor (8_c) representations are permuted by an outer automorphism of order 3. The B4 root system has 32 roots (±e_i ± e_j, ±e_i), with the 8 short roots (±e_i) forming the vector rep of SO(8). The staggered fermion doubling produces exactly the 8+8 = 16 components, matching the 8_s ⊕ 8_c decompositi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com