Standard Model Gauge Group from Exceptional Jordan Algebra and F4 — E8 Intelligence Research

FINDING: Standard Model gauge group \( SU(3) \times SU(2) \times U(1) \) constructed from exceptional Jordan algebra \( \mathfrak{h}_3(\mathbb{O}) \) and its automorphism group \( F_4 \), via subalgebra chains \( \mathfrak{h}_2(\mathbb{C}) \subset B \subset \mathfrak{h}_3(\mathbb{O}) \). MATH: - Exceptional Jordan algebra: \( \mathfrak{h}_3(\mathbb{O}) \) — 3×3 Hermitian octonion matrices, dimension 27. - Automorphism group: \( \text{Aut}(\mathfrak{h}_3(\mathbb{O})) = F_4 \), a compact exceptional Lie group of dimension 52. - Subalgebra chain: \( X \cong \mathfrak{h}_2(\mathbb{C}) \) (complex 2×2 Hermitian matrices) embedded in \( B \subset \mathfrak{h}_3(\mathbb{O}) \). - Gauge group emerges as stabilizer of this chain within \( F_4 \): \( \text{Stab}_{F_4}(X \subset B) = SU(3) \times SU(2) \times U(1) / \mathbb{Z}_6 \). - Key constants: dimensions of \( F_4 \) (52), \( E_6 \) (78), \( \mathfrak{h}_3(\mathbb{O}) \) (27). No explicit numeric ratios like 0.618 appear in the c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com