Nevertheless, the relationship between E(v, A) and F(ρ, j p ) is sufficient to establish the Vignale-Rasolt formulation as a rigorous extension of DFT to systems in an external magnetic field. To obtain a convex formulation, however, the change of variables u = v + |A| 2 /2 is needed, imposing a formulation of the theory where the potential space can absorb the norm squared of the vector potential. 629 Such a formulation of CDFT inherits the mathematical structure of standard DFT, only lacking the uniqueness provided by a Hohenberg-Kohn result.