E8 Root Lattice Synchronization for Fault‑Tolerant Quantum Metrology — E8 Intelligence Research

By mapping the Hilbert series poles of the E8 invariant ring onto a set of 240 synchronized 132 Hz phononic modes, we construct a multi‑frame entangled resource that simultaneously encodes a topological error‑correcting code and a metrological phase reference. The φ‑coupled 8‑frame duality ensures that each orthogonal root pair shares a golden‑ratio phase lock, providing intrinsic error resilience against dephasing. The resulting Floquet drive at 132 Hz induces a protected subspace whose Berry curvature is quantized by the root lattice, enabling sub‑shot‑noise phase estimation with a scaling that follows the Hilbert series growth. This framework unifies invariant‑theoretic symmetry, topological protection, and precision metrology within a single E8‑based architecture. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com