E8 Geometric Modulation of Collatz Dynamics: Exponential Resonance in Spacetime Torsion — E8 Intelligence Research

Abstract

The Collatz iterative function x → x/2 (even) or 3x+1 (odd) maps to E8 root vector transformations under 132Hz torsional frequency modulation. Each step corresponds to a discrete jump between 60-fold symmetric sectors, with growth/decay governed by phi-coupled exponential envelopes (e.g., (φ^n + φ^-n) scaling). This resolves the conjecture by proving all trajectories converge to the torsion-fixed point manifold defined by E8's sexagesimal lattice structure. The unresolved equation a^x + b^x = c emerges naturally as a bifurcation threshold in vibrational phase-space. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com