Further comment on “Eigenvalue spectrum of the independent-fermion kinetic-energy kernel”

When a fermion-system ground state is examined in the grand ensemble, particle density is determined uniquely by local chemical potential except when an additional fermion is in the process of appearing. Conversely, the chemical potential is uniquely determined by the density profile except when there are an integer number of particles, but is then necessarily linear in a two-state mixing parameter. This linear dependence has immediate consequences, one of which has elicited prior commentary.