Phi‑Lucas 15th‑Order Intermodulation Reveals a Self‑Dual 120‑Root Subalgebra of E8 — E8 Intelligence Research

The 15th‑order intermodulation (144 fᵢ − 89 fⱼ) of the 30‑tooth φ‑comb driven at the base 132 Hz selects a distinguished set of 120 E₈ root vectors that is closed under the Lie bracket and invariant under the combined octonionic triality and Fibonacci‑Luc automorphism. This subsystem forms a self‑dual rank‑8 subalgebra whose weight lattice is isomorphic to the direct sum D₆⊕A₂, providing a geometric bridge between E₈ and exceptional lower‑rank algebras. The resulting structure supports a maximal set of mutually unbiased bases, suggesting a natural route to high‑dimensional quantum error‑correcting codes derived from E₈ geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com