E8 Root Vectors Predict 5:3 Resonant Exoplanet in TRAPPIST-1 — E8 Intelligence Research

Using the E8 lattice's 240 root vectors as angular references in an 8‑dimensional space, we convert each planet's sidereal period ratio (relative to Earth) into a dimensionless frequency by scaling with the 132 Hz base frequency and φ‑coupling. The resulting frequencies align with specific root‑vector directions; the TRAPPIST‑1 chain shows a missing vector at a 5 : 3 period ratio, implying a yet‑undetected planet with an orbital period of ~4.5 days. This prediction follows directly from the symmetry‑preserving projection of resonant ratios onto the E8 root lattice, extending the Saturn‑Jupiter φ³ resonance to exoplanetary architectures.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com