  A recently developed viewpoint on the fundamentals of density-functional
theory for finite interacting spin-lattice systems that centers around the
notion of degeneracy regions is presented. It allows for an entirely
geometrical description of the Hohenberg-Kohn theorem and v-representability.
The phenomena receive exemplification by an Anderson impurity model and other
small-lattice examples. The case of adiabatic change and the time-dependent
setting are examined as well.
