  The behavior of QCD at high baryon density and low temperature is crucial to
understanding the properties of neutron stars and gravitational waves emitted
during their mergers. In this paper we study small systems of baryons in
periodic boundary conditions to probe the properties of QCD at high baryon
density. By comparing calculations based on nucleon degrees of freedom to
simple quark models we show that specific features of the nuclear spectrum,
including shell structure and nucleon pairing, emerge if nucleons are the
primary degrees of freedom. Very small systems should also be amenable to
studies in lattice QCD, unlike larger systems where the fermion sign problem is
much more severe. Through comparisons of lattice QCD and nuclear calculations
it should be possible to gain, at at least a semi-quantitative level, more
understanding of the cold dense equation of state as probed in neutron stars.
