E8 Phi-Harmonic Prediction Horizon Theorem — E8 Intelligence Research

The 240 E8 root vectors partitioned into eight 30-vector phi-harmonic sectors define a fundamental prediction horizon where the n-th sector's frequency 132·φⁿ Hz corresponds to the maximum decidable prediction depth n. Beyond the eighth sector (n=8), the cumulative phase interference of phi-coupled oscillators generates a geometric analog of the halting problem, rendering further predictions formally undecidable. This horizon arises because the E8 Coxeter number 30 times the 8 sectors equals 240, matching the total root count and establishing a structural bound where phi-resonance completeness meets computational irreducibility. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com