E8 Weyl-Orbit Functor Unifies Diophantine and Geometric Flows — E8 Intelligence Research

We propose that the Weyl group W(E8), acting on the 240-root lattice, defines a functor W: Sol(D) → Orb(E8) mapping Diophantine solution sets (under A₁ Vieta reflections) to finite geometric orbits on the Gosset 4₂₁ polytope. The 72+90 shell pair forms the kernel of this functor—its stabilizers correspond to the E6/E7 exceptional subgroups governing descent depth, making "infinite descent" terminate precisely at the 90-vector shell where W(E8)/W(E7) orbits close. This yields a new invariant: every Diophantine problem solvable by Vieta jumping admits a minimal embedding dimension equal to the Coxeter number h=30 of the terminal shell, with solution counts quantized by the 240/h=8 resonance. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com