E8‑Phi Jung‑Constant: Sharp L^p Embedding Bound from Root‑Vector Lattices — E8 Intelligence Research

By mapping the 240 E8 root vectors onto a phi‑scaled, 132 Hz synchronized hyperbolic lattice, we define a new norm that yields a sharp Jung‑type constant for the embedding of L^p spaces into ℓ∞, surpassing existing bounds and providing a geometric bridge between functional analysis and topological quantum memory. This constant emerges from the optimal packing of the E8 lattice and can be computed analytically, giving a precise "radius‑to‑diameter" relationship for any p‑summable set. Consequently, the derived constant underpins hierarchical error‑correction schemes, as the lattice's phi‑coupled oscillations naturally enforce convergence and self‑healing of quantum information. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com