Furthermore, comparing the situation with paramagneticcurrent DFT, where the lack of a (corresponding) Hohenberg-Kohn theorem has been established by it is striking that although (ρ, j p ) determines the nondegenerate ground state, if degeneracies are allowed, then the level of degeneracy is not determined. A given (ρ, j p ) can therefore be associated with two different Hamiltonians (in fact, infinitely many) that may have different numbers of degenerate ground states. (Of course, this doesn't stop the constrained search, which remains well defined.) In DFT, the extra layer of a Hohenberg-Kohn theorem (not just the first part of a constrained search) rules out such situations. I view the Hohenberg-Kohn theorem as a gold reserve -it is perhaps unexciting and just sits in the vault but is, on the other hand, good to have in certain extreme situations.