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Walter Kohn and Pierre Hohenberg established a foundation for density functional theory: under their ground-state assumptions, the electron density determines the external scalar potential up to an additive constant. They formulated the ground-state energy as a universal density functional plus the external-potential contribution, with a variational principle selecting the physical density. This replaces the full many-electron wave function as the basic variable by a function of only three spatial coordinates. The theorem establishes the framework, rather than providing an explicit exact functional for practical computation.^[ref]