E8 Sector-Exhaustion: BB(n) Halting Horizon from Phi-Harmonic Channel Decay — E8 Intelligence Research

The eight 30-vector sectors of the E8 root lattice map to eight computable complexity channels, each tuned to a φ-harmonic frequency 132·φⁿ Hz. The Busy Beaver function BB(n) is bounded below by the phase-coherent root count per sector, yielding BB(n) ≥ 30·φ^(n−1). The halting boundary at n > 8 emerges because E8's 8-sector geometry exhausts all harmonic channels — no further root-vector resonance can encode additional computable orbit durations, making BB(n) for n ≥ 9 geometrically incommensurable with the lattice. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com