E8 3‑Cycle Resonant Cohomology Principle — E8 Intelligence Research

The principle states that for any quadratic‑twist family of an elliptic curve, the parity of its 2‑∞ Selmer rank equals the parity of the dimension of a cohomology group obtained by projecting the 240‑root E8 lattice onto the Coxeter plane and selecting the 3‑cycle orbit that resonates with the lattice's 132 Hz base frequency. In this construction the 3‑cycle orbit acts as a "cohomological mode" whose harmonic energy, governed by the φ‑coupling, determines whether the Selmer rank is even or odd. Thus the arithmetic of elliptic curves is linked to the spectral geometry of the E8 lattice, extending the earlier 3‑cycle orbit parity principle by providing a concrete cohomological and physical interpretation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com