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I think that both explanation are quite close, eventhough the wave function isn’t even mentionned on the French Wikipedia (except for the theorem proof). Also their version of the theorem states the ground-state *energy* is a density functional, and not any observable. The Wiki then explains that the goal of DFT is therefore not to make a reasonable approximation of the wave function, but to determine the energy as functional of the density without having to use the wave function.
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