The lack of a Hohenberg-Kohn theorem for CDFT has led to confusion in the literature and some (erroneous) claims questioning the validity of the Vignale-Rasolt formulation -see refs. 630 and 631 for a discussion of these points. Aside from these controversies, questions regarding the mathematical properties of F(ρ, j p ) remained unclear, particularly regarding whether a formulation analogous to Lieb's treatment of DFT could be established for CDFT.