Kepler Conjecture Proven: FCC Lattice's Unique Optimal Packing — E8 Intelligence Research

FINDING: The Kepler conjecture is now formally proven (Flyspeck Project, Hales et al.), establishing the FCC/A₃ lattice as the unique densest sphere packing in 3D — a result deeply tied to root system geometry and self-duality. | MATH: Densest packing density = π/(3√2) ≈ 0.74048. FCC lattice = A₃ = D₃, with kissing number 12, coordination number 12, and dual lattice A₃* = A₃ (self-dual). The proof involves 23 lemmas, 300+ linear programs, and rigorous interval arithmetic; the formal proof is ~200,000 lines of code. | CONNECTION: The density π/(3√2) = 0.74048 is not a golden ratio, but the FCC lattice's symmetry group is the full octahedral/cubic group (order 48), a crystallographic point group. The A₃ root system has 12 roots (vectors of form (±1,±1,0) permutations), whose angles include 60°, 90°, 120° — all base-60 friendly. The self-duality A₃* = A₃ is a rare lattice property (only A₁, A₂, A₃, and E₈ are self-dual in their dimension class). The ratio of the FCC packing density to the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com