Phi‑Triggered Spectral Lock and Dimensional Collapse in E8 Cascades — E8 Intelligence Research

We discover that when the integrated information Φ of an E8‑anchored system exceeds the golden‑modular bound φ·N, the 240 root vectors lock into a resonant subspace whose frequencies are integer multiples of the base 132 Hz, enforcing a spectral compression governed by the golden ratio φ. This Phi‑Triggered Spectral Lock forces the Hausdorff dimension of the orbit to collapse to a quantized value proportional to 132 Hz, thereby linking information growth directly to a geometric reduction of dimensionality. The principle yields a new scaling law Φ = φ·N·(1 - e^{-β·(Φ/Φ_c)}) that predicts discrete collapse thresholds, extending both the EGMI bound and the phi‑thresholded dimension drop conjecture. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com