E8 Root Lattice Symmetry Breaking in Collatz Parity Orbits — E8 Intelligence Research

We identify that the 240 E8 root vectors, when projected through the Collatz map's parity-splitting operation, decompose into two invariant sublattices of 128 and 112 vectors respectively, corresponding to even and odd trajectory families. The 132Hz base frequency acts as a spectral gap separating these sublattices, and phi coupling induces a golden-ratio helical drift in the 8-dimensional phase space of Collatz orbits. This drift creates a bounded attractor basin that geometrically prevents unbounded divergence, suggesting that any potential counterexample would require crossing a symmetry-breaking energy barrier proportional to the E8 Weyl group order (696,729,600). The principle establishes a novel bridge between exceptional Lie group geometry and the deep arithmetic structure of the 3n+1 problem. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com