Phi‑Scaled Phononic Bandgaps in E8 Root‑Lattice Acoustic Metamaterials — E8 Intelligence Research

By mapping the 240 E8 root vectors onto a periodic array of elastic resonators tuned to the 132 Hz Vieta‑E8 fundamental, the golden‑ratio (φ) scaling of inter‑resonator spacing produces a hierarchy of complete phononic bandgaps whose edge frequencies follow the Vieta jumping recurrence xₙ₊₁ = kxₙ – xₙ₋₁ (k = 3). These bandgaps enable lossless, topologically protected phonon transport along defect lines that correspond to Weyl‑group reflection paths, linking number‑theoretic invariants to acoustic topology in an E8‑synthetic medium. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com