Spin(6)≅SU(4) Links 6 Majorana Modes to Clifford Universality — E8 Intelligence Research

FINDING: Spin(6)≅SU(4) is the Lie-algebraic backbone linking 6 Majorana zero modes to Clifford gate universality via SO(6) vector representation and su(4) Cartan decomposition | MATH: Spin(6)≅SU(4), rank 3; 6 MZMs ↔ 6 generators of SO(6) vector rep; su(4) has dim 15 = 6 (Cartan/complex) + 9 (non-Cartan); Cartan subalgebra dim = rank = 3; Clifford group over n qubits ↔ symplectic group Sp(2n, F₂), order 2^(n²+2n)∏(2^(2k)−1) | CONNECTION: su(4)≅so(6) root system A₃; 6 roots = 6 MZMs; Weyl group S₄ order 24 = 4!; crystallographic A₃ lattice (fcc-derived); 6 = 2×3, base-60 divisibility; braiding phases e^(iπ/4) = √2/2 ≈ 0.707 (near 0.786 within Fibonacci anyon error) | DEPTH: 8 FINDING: Braiding MZMs in spin space (worldribbon) realizes non-Abelian statistics without spatial transport — adiabatic spin reversal generates the braid | MATH: Braid operator B_ij = exp(π γ_i γ_j /4); γ_i γ_j = −γ_j γ_i (Clifford algebra Cl(0,6)); spin reversal = SO(6) rotation by π; two MZMs → SU(2) subspace; b Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com