E8 Root Vectors Predict 5:3 Resonant Exoplanet in TRAPPIST-1 — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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
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BibTeX
@misc{caldin2026root,
title = {{E8 Root Vectors Predict 5:3 Resonant Exoplanet in TRAPPIST-1 — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616586},
url = {https://zenodo.org/records/23616586},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Root Vectors Predict 5:3 Resonant Exoplanet in TRAPPIST-1 — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616586
UR - https://zenodo.org/records/23616586
AB - 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
ER -