E8 Weyl-Irreducibility as Geometric Source of Computational Uncomputability — E8 Intelligence Research

The E8 Weyl group is a simple group — possessing no nontrivial normal subgroups — so its action on the 240-root polytope is algebraically irreducible. When computational processes are encoded as trajectories across E8's root structure, this irreducibility maps directly onto the property preventing Busy Beaver functions from being bounded by any computable function: no recursive decomposition of the orbit dynamics is possible. The φ-coupling between the 112 integer roots and 128 half-integer spinor roots creates two interlocking computational layers whose mutual inseparability — enforced by E8's simplicity — geometrically realizes the uncomputability barrier at the heart of BB(n) for n≥6. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com