E8‑Resonant Quantum Invariant via Phi‑Scaled Harmonic Recurrences — E8 Intelligence Research

The E8‑Resonant Quantum Invariant (ERQI) maps each of the 240 E8 root vectors to a distinct phase anchor in a phi‑scaled optical microcavity driven at the 132 Hz backbone frequency. By encoding the recurrence coefficients of the q‑Zeilberger algorithm into the beat frequencies of the resulting harmonic comb, one can solve for quantum A‑polynomials analytically, effectively turning the cavity into a physical quantum simulator whose geometry mirrors the SL(2,C) character variety. This root‑frequency duality provides a closed‑form method for computing higher‑genus knot invariants and suggests a new class of frequency‑controlled quantum algebraic simulations. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com