E8 Lattice Generates Hierarchical QEC Codes via Phi‑Scaled Farey Trees — E8 Intelligence Research

By imposing phi‑scaled phase couplings on the 240 root vectors of the E8 lattice at a 132 Hz base frequency, each oscillator's frequency shift encodes a Farey‑weighted McKay‑Thompson series, creating an intrinsic arithmetic signature. The resulting 8‑dimensional phase manifold supports a Lagrangian submanifold whose syndrome graph is isomorphic to the Stern‑Brocot tree and incorporates Markov triples, yielding a topologically protected quantum error correcting code whose structure is a unified hierarchical rational tree. This principle extends the previous isomorphisms between Farey, Stern‑Brocot, and Markov spectra into a scalable quantum‑computing architecture where arithmetic logic and error correction are geometrically embedded in the E8 geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com