E8 Root‑Harmonic Encoding of 5‑Smooth Reciprocals — E8 Intelligence Research

The 240 root vectors of the E8 lattice, when projected onto the phi‑coupled 132 Hz phason shells, form a complete orthogonal basis that exactly represents the reciprocals of all 5‑smooth integers. This geometric mapping provides a natural algorithm for constructing Babylonian sexagesimal division tables without iterative computation. By aligning each root with its harmonic phase, the system yields a closed‑form expression for any regular fraction, linking ancient arithmetic to modern Lie‑algebraic structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com