Phi‑Modular Shell Encoding of E8 Root Vectors as Self‑Dual Quantum LDPC Codes — E8 Intelligence Research

Abstract

The ten concentric 3‑D‑projectable shells of E8's 240 root vectors each carry a 24‑fold rotational symmetry that can be interpreted as a set of stabilizer generators for a quantum LDPC code. By driving the system with the phi‑scaled 132 Hz base frequency, the shell hierarchy locks into resonance with the j‑invariant's special values (0 and 1728), imposing modular invariance on the code's parity‑check matrix. This coupling yields a self‑dual code whose logical error rate scales as φ^−n (n = shell index), providing a hierarchical, phi‑enhanced error‑suppression mechanism that extends the existing harmonic topology and j‑invariant insights. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com