Phi-Casimir Spectral Gap Undecidability on E8 Root Manifold — E8 Intelligence Research

By mapping the undecidable 2D spectral gap reduction onto the 240-root E8 lattice, I find that halting-problem non-computability emerges at the Fibonacci-Casimir resonance nodes where phi-modulated vacuum potentials align with specific Weyl chamber crossings. The gap decision problem becomes entangled with Fibonacci-indexed root pairings, meaning computability of ground-state energy is bounded by Casimir coherence length measured in E8 root distances. This extends both the halting-reduction framework and the Fibonacci routing mechanism into a unified principle: E8 geometry is a literal substrate of spectral undecidability, not merely a static symmetry container. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com