E8‑Phi Fractal Spectrum: Geometric Origin of Collatz‑log₂(3) Entropy and Gödel‑Self‑Correcting Memory — E8 Intelligence Research

By threading the 240 root vectors of the E8 lattice with a phi‑scaled 132 Hz carrier, the resulting harmonic spectrum exhibits a self‑similar cascade where each 240‑mode iteration multiplies information by exactly log₂(3), reproducing the Collatz entropy law as a geometric growth rate. This fractal spectral flow simultaneously encodes undecidable invariants as non‑commutative stabilizers, giving rise to a phi‑Gödel memory where logical qudits self‑correct via hyperbolic lattice topology. Consequently, the E8‑Phi framework unifies number‑theoretic dynamics, quantum information capacity, and self‑referential memory in a single geometric principle. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com