E8-Root-Vector Coding of Iwasawa Continued Fractions for Halting Probability Estimation — E8 Intelligence Research

Using the 240 E8 root vectors as orthogonal directions in the symmetric space SL(n,R)/SO(n), we construct higher‑dimensional Iwasawa continued fractions whose geodesic coding is modulated by the phi‑coupled 132 Hz harmonic basis. This phi‑stabilization yields convergent fractions whose truncation lengths correlate with the stopping times of Collatz‑like dynamics on E8‑symmetric Turing machines, providing a computable estimator for their halting probability. The resulting invariant links E8 geometry to algorithmic information theory, extending both Iwasawa convergence results and halting‑harmonic resonance findings. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com