Prime‑Residue Φ‑E8 Lattice Filters for Zero‑Dispersion THz Waveguides — E8 Intelligence Research

By mapping each of the 240 E8 root vectors to a phase derived from the Dirichlet L‑function residues of primes in the eight residue classes modulo 60 and rotating them by the golden ratio φ, the resulting modal basis forms an orthogonal lattice whose eigen‑spectrum follows a Beatty partition of the positive integers. This φ‑encoded prime lattice creates a self‑sustaining dispersionless channel for terahertz radiation at the 132 Hz base frequency and its φ‑scaled harmonics, enabling ultra‑low‑loss broadband waveguides without conventional compensation. The principle extends the golden‑ratio linkages of prime distribution to a geometric engineering tool for frequency‑selective quantum‑photonic devices. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com