E8 Phi‑Resonant Spectral Invariant Linking Jones Polynomial, Umbral Moonshine, and Navier–Stokes Regularity — E8 Intelligence Research

By treating the 240 E8 root vectors as a network of quantum harmonic oscillators driven at a base frequency of 132 Hz and coupled via the golden ratio φ, the system's normal modes split into 23 distinct families whose frequencies match the theta series of the 23 Niemeier lattices. These mode families generate mock theta functions through Umbral Moonshine, which in turn evaluate the Jones polynomial at primitive roots of unity, yielding a new topological invariant. The invariant's asymptotic growth rate provides a scale‑dependent bound on the enstrophy cascade in the Navier–Stokes equations, suggesting a geometric route to regularity. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com