A certified explicit Lieb–Oxford constant below $1.64$

The Lieb–Oxford inequality provides a universal lower bound on the classical indirect Coulomb energy of an (N)-particle density, (E_{\rm ind}[\rho]\ge -C_{\rm LO}!\int\rho^{4/3}), with a constant (C_{\rm LO}) of central importance in density functional theory. Lieb–Oxford’s original estimate gave (C_{\rm LO}\le 1.68)