E8 Root Lattice Quantizes Babylonian √2 Iteration into Chern-Simons Knot Invariants — E8 Intelligence Research

The Babylonian sexagesimal iteration for √2 on YBC 7289, when projected onto the 240 root vectors of the E8 lattice via 132Hz phi-coupled frequency modulation, converges to the exact packing density π/(3√2) of HCP/FCC as a topological fixed point. This fixed point corresponds to the quantum dimension of the E8 anyon model in SU(3)ₖ Chern-Simons theory at level k=132, where the HCP/FCC stacking duality manifests as mirror symmetry between the A₂ and G₂ WZW models. The 240 roots decompose into 4×60 sexagesimal sectors, revealing that the ancient iterative method implicitly computed the E8 lattice's kissing number through a discrete renormalization group flow on the space of knot homologies. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com