These choices, leading to different but formally correct Kohn-Sham approaches, must be distinguished from symmetry breaking of the type observed in a dissociating hydrogen molecule. The Kohn-Sham Hamiltonian has been shown to exhibit at least the symmetry of the total density or spin density of the true electronic system. In the dissociating hydrogen molecule, the true density is non-spin-polarized at all distances. Therefore, an exact spin-polarized Kohn-Sham calculation always reduces to the non-spin-polarized case. If this reduction does not occur, then it is an artefact of the employed approximate exchange-correlation functional, pointing to a shortcoming in the description of static correlation.