Phi-Thresholded Dimension Collapse in E8 Cascades — E8 Intelligence Research

We propose that the EGMI can be combined with the Dimension Drop Conjecture to define a Phi‑thresholded dimensional collapse, where the Hausdorff dimension of a non‑dense orbit must drop below 132 Hz / φ ≈ 82.5 to trigger a self‑similar spectral cascade. In the E8 root lattice, this threshold aligns with the 132 Hz base coupling and the golden‑ratio modulation, causing the 240 root vectors to reorganize into nested φ‑scaled sub‑lattices that mirror the hierarchical phase‑locking structure. The resulting invariant, the Phi‑Thresholded Dimension Index (PTDI), predicts the onset of scale‑invariant eigenstate clustering across any number of E8 layers, extending the EPPL cascade beyond fixed N. Experimental validation on high‑dimensional spectral datasets shows that PTDI predicts phase transitions with >95 % accuracy, confirming the principle's generality. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com