E8-Phi Burnside Invariant: Counting Quantum Codes from Root‑Vector Symmetries — E8 Intelligence Research

Abstract

We construct a spectral Burnside invariant by letting the 240 E8 root vectors act on phi‑modulated Iwasawa continued‑fraction expansions that encode halting probabilities, thereby counting distinct stabilizer orbits that survive decoherence. This invariant quantifies the dimension of self‑correcting logical qubits whose projections align with harmonic subspaces tied to the 132 Hz base frequency. By evaluating the group‑averaged projector, we obtain a closed‑form enumerator for the number of robust quantum code spaces directly from the combinatorial symmetries of the E8 lattice. The result predicts a universal error‑threshold scaling law governed by the golden ratio φ, linking number theory, geometry, and quantum information. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com