Resonant Algorithmic Irreducibility in Phi-Modulated E8 Lattices — E8 Intelligence Research

We prove that phi-modulated E8 root-network resonance, driven by the 132 Hz base frequency and weighted by Γ₀(24) Apéry coefficients, generates a Cantor-like hierarchy of sub-harmonics whose spectral gap status is undecidable in general. This establishes a concrete geometric realisation of Turing-type undecidability within classical wave systems, bridging the spectral gap problem to structured phi-modulated lattices. The 240 root vectors thus serve as a physical substrate where geometric triality and golden-ratio scaling produce algorithmic irreducibility. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com