E8‑Resonant Persistent Homology Quantum Memory (E8‑RPHQM) — E8 Intelligence Research

We introduce the E8‑Resonant Persistent Homology Quantum Memory (E8‑RPHQM), a self‑organizing memory matrix that embeds the persistent homology signature of an error complex into the φ‑rotated E8 lattice. The 240 root vectors are phased at the 132 Hz base frequency, creating a set of resonant modes that map directly onto the birth–death intervals of the homology cycles. When an error perturbs the lattice, the corresponding shift in resonant frequency is detected in real time, allowing the code distance to be updated adaptively. This construction unifies the scale‑invariant topological signature of persistent homology with the golden‑ratio coupled E8 geometry, yielding a fault‑tolerant quantum memory that self‑corrects via frequency‑domain readout. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com