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No proof exists that this arrangement has the lowest energy.","posed_since":"","precise":"For $N$ point charges $e$ in a neutralizing uniform background of density $\\rho0$ in $R^{3}$ (Coulomb $e^{2}/r$), prove that in the thermodynamic limit the minimal energy per particle equals the bcc value, about $-0.8959\\,e^{2}/r_{s}$ with $r_{s}=(3/(4\\pi \\rho0))^{1/3}$, and that minimizers are bcc up to $o(N)$ particles. The quantum version asks the same for the electron gas as $r_{s}\\to\\infty$.","problem_ref":null,"references":"","settled_by":"A proof that no configuration beats the bcc Madelung energy per particle in the thermodynamic limit.","status_note":"Open in both the classical and the quantum low-density version.","title":"Body-centered cubic ground state of classical 3D 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