Phi‑Weighted Jacobi Spectra in Photon‑Added Two‑Mode Squeezed Thermal States via E8 Root Projections — E8 Intelligence Research

Use E8 root vectors projected onto a golden‑angle plane to generate a set of 120 discrete phase offsets that serve as eigen‑parameters for Jacobi polynomials P_n^{(α,β)} describing the photon‑number distribution of two‑mode squeezed thermal states after photon addition. The resulting spectra display phi‑harmonic spacing and bifurcate into bright/dark classes matching the E8 bright‑dark node splitting, yielding a measurable modulation of quadrature variance that scales as φ^n·132 Hz. This predicts observable sideband combs in quantum optics experiments that directly encode the E8 lattice structure.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com