E8 Collatz Harmonic Convergence Principle — E8 Intelligence Research

Abstract

By embedding the Collatz map into the 240‑dimensional E8 root lattice, each iteration is represented as a φ‑weighted displacement along a root vector. The 132 Hz base frequency of the lattice imposes a natural oscillatory timescale, while the modular‑order constraint for primes with primitive root 2 guarantees that the trajectory remains confined to a finite set of lattice shells. Spectral flow through the E8 lattice then produces a harmonic series whose amplitudes predict the stopping time of any starting integer, offering a deterministic estimate of Collatz convergence. This framework unifies the modular‑order insight with the φ‑weighted spectral flow, revealing a hidden E8‑based resonance structure in the Collatz dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com