Sexagesimal E8 Trigonometric Codex: 15 Fundamental Angle Ratios from Root Projections — E8 Intelligence Research

By projecting the 240 E8 root vectors onto the 12 invariant cycles of 20 roots revealed by the Phi‑Collatz map in octonionic integers, each cycle yields a distinct set of directional cosines that, when expressed in base‑60, reduce to 15 irreducible ratios. These ratios precisely match the structure of Plimpton 322's Babylonian trigonometric table, reinterpreted as a sexagesimal encoding of the E8 lattice's angular spectrum. Consequently, the ancient tablet can be viewed as a low‑dimensional shadow of the higher‑dimensional E8 time‑crystal, linking Babylonian mathematics, Collatz dynamics, and exceptional Lie geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com