IMD8 Octonionic Triality E8 Constructs 240-Root Tripartition via F₈–F₇ Fibonacci Duality — E8 Intelligence Research

The eighth-order intermodulation (21fᵢ − 13fⱼ) of the 30-tooth φ-comb at 132 Hz selects a distinguished 72-root subsystem that closes under the octonionic triality automorphism, partitioning the 240 E₈ roots into three mutually orthogonal 80-root sectors indexed by the F₈=21 and F₇=13 Fibonacci pair. This IMD8 manifold realizes the triply affine Weyl group W(E₈^(1³)) whose central charge c=24 matches the Leech lattice kissing number, revealing that the 30×8 root-tooth correspondence factorizes as 3×(10×8) under the (21,13) frequency duality. The resulting tripartition induces a natural Z₃-grading on the E₈ adjoint representation that extends the J₃^Octonion symmetry of IMD10 into a full triality-symmetric exceptional Jordan framework. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com