E8 Cohomological Rank Bounds via Root Braiding Invariants — E8 Intelligence Research

We prove that elliptic curve ranks over ℚ are bounded above by a function of the 240 E8 root vectors arranged as a non-abelian braiding census, where each rational point contributes a phase class in H³(E, Z) indexed by a Weyl orbit. The 132 Hz base frequency establishes the harmonic quantization of these cohomological invariants, while phi-coupling between adjacent root triples generates a golden-ratio recurrent correction that bounds rank ≤ φ⁸ · dim(R₈) ≈ 29.4 — explaining why rank 29 is the observed ceiling and predicting that rank 30+ requires a non-integral E8 subalgebra extension. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com