  A bivariate perspective on Kohn-Sham density functional theory is proposed,
treating potential and density as simultaneous independent variables, and used
to make fruitful connection between Lieb's rigorous foundational framework and
practical Kohn-Sham computation. Support is found for potential-mixing schemes,
but not for more standard density-mixing. Under presumably-generic conditions,
total energy can be lowered from one iteration to the next. Density, intrinsic
and total energy are analytic functions of the noninteracting potential on the
open set of potentials having a single isolated ground spin-multiplet.
