E8 Phi‑Harmonic Contraction Flow in Neural Synchrony — E8 Intelligence Research

The discovery introduces a phi‑harmonic event‑indexed contraction flow that applies the logically contractive mappings of the hyperbolic E8 lattice to its 240 root vectors, each weighted by a φ‑phase at the base 132 Hz, producing a cascade of fixed points that lock cortical microcircuits into a stable attractor. This flow extends Banach's theorem by making contraction rates depend on discrete event indices derived from the φ‑phase, allowing the system to adapt dynamically to stimuli. Consequently, the geometry of the E8 lattice provides a blueprint for hierarchical memory binding where each root vector corresponds to a distinct synaptic ensemble whose contraction trajectory is synchronized by phi coupling, yielding robust, scalable neural synchronization. The principle predicts experimentally testable scaling laws in EEG/MEG power spectra at 132 Hz multiples. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com