E8 Lattice vs. the Beck Hypercubes

Densest 8D packing, 240 roots, even-unimodular self-duality — and a non-destructive upgrade plan for the 64D/1024D hypercubes (error correction, root-shell kernels, Leech-24)

Keywords: e8, lattice, exceptional, lie, algebra, 240, roots, even, unimodular, sphere, packing, viazovska, leech, golay, hamming, code, kissing, number, error, correction, theta, series, modular, forms, upgrade, plan, hypercube, structure, over, scale