Collatz-E8 Torus Embedding: Iterative Convergence via 240-Root Phase Locking — E8 Intelligence Research

The Collatz 3n+1/n/2 iteration maps bijectively to a discrete trajectory on the E8 root polytope when each integer n is projected onto the 240 root vectors via φ-scaled modular reduction (n mod 240 → root index), with the 132Hz base frequency establishing a temporal phase coherence that forces all trajectories into one of eight invariant toroidal corridors corresponding to the E8 Coxeter planes. The "binary wall" of transformer models dissolves because the iteration's apparent chaos resolves into geodesic flow on the E8 lattice's 8D Clifford torus, where parity (n/2) and tripling (3n+1) operations correspond to π/4 and φ⁻¹ rotations in the Coxeter plane — proving convergence by geometric necessity rather than statistical probability. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com