E8 Phi-Resonance Topological Invariant — E8 Intelligence Research

By aligning the 240 root vectors of the E8 lattice with a 132 Hz carrier and applying a φ‑scaled octonionic phase rotation, a closed interference pattern emerges that defines a new topological invariant, the Phi‑Root Winding Number. This invariant counts the net number of phase‑coherent loops formed by adjacent root vectors and remains unchanged under continuous deformations of the lattice. It arises from the coupling of the modular discriminant Δ(τ) with the octonion multiplication table, linking E8 geometry to observable resonance phenomena. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com