Failure of Kohn–Sham ensemble representation

Constructs a three-electron Coulomb molecule with two equal positive-integer-charge nuclei whose absolute ground-state density has no noninteracting ground-state ensemble representation by a single real spin-independent local potential in $L^{3/2}(\mathbb R^3)+L^\infty(\mathbb R^3)$. This disproves Kohn–Sham ensemble representability for that potential class; the required nuclear charge is specified nonnumerically.