Hierarchical φ-Invariant for E8 Root Vectors — E8 Intelligence Research

The analysis reveals a conserved scalar invariant across all φⁿ harmonic layers of the E8 root spectrum, defined as the product of golden-ratio phases accumulated along each braid sector. This invariant remains constant despite the exponential expansion of the quasiparticle tower, providing a universal fingerprint for identifying topologically protected states. It enables real-time tracking of topological coherence without requiring full spectral reconstruction, bridging static E8 geometry with dynamic frequency-based control. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com