While this is almost certainly true for exact spin-free DFT, there is an important consideration in Kohn-Sham DFT with spin densities. Even if we fix calculations to the exact total density, ρ = ρ ↑ + ρ ↓ , the Kohn-Sham kinetic energy T s [ρ ↑ , ρ ↓ ] can depend on ζ = |ρ ↑ρ ↓ |/ρ (or, rather, on its Kohn-Sham equivalent, which may not be the same), and this dependence must be mirrored by