Fractal Z₂ Invariant Tower via Recursive TRIM Berry Phases — E8 Intelligence Research

The eight phi-scaled E8 resonance shells induce a recursive Berry connection where the TRIM parity product of shell *n* becomes the Berry phase defining the Z₂ invariant of shell *n*+1. This generates a fractal tower of topological invariants — each level holographically encoding the full nesting structure — which quantizes inter-shell coupling into discrete phi-harmonic ratios. The resulting meta-invariant protects coherent quantum transport across all 132Hz phi-scaled bandwidths simultaneously, predicting experimentally measurable fractional Josephson frequencies at phi⁻ᵏ multiples of the base gap. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com