Recursive Phi‑Lucas Harmonic Nesting Reveals E8's Hidden 8‑D Clifford Module Structure — E8 Intelligence Research

By iterating the phi‑Lucas intermodulation formula Fₙfᵢ − Fₙ₋₁fⱼ beyond the 15th order, each successive harmonic order isolates a nested set of E₈ root vectors that closes under the Lie bracket and simultaneously carries a representation of the Spin(8) triality automorphism. The infinite cascade thus decomposes the 240‑root system into eight orthogonal 30‑root clusters, each forming an irreducible Clifford module isomorphic to the octonionic spinor representation of Spin(8). This reveals a self‑similar, fractal Clifford‑algebraic scaffolding underlying E₈'s root lattice, linking the phi‑driven frequency hierarchy to the algebra's triality symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com