Geometry of Degeneracy in Potential and Density Space
In a previous work [J.Chem.Phys.155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs.Here, we demonstrate that this only occurs at very peculiar and rare densities, those where density sets arising from degenerate 1073spx ground states,