  I have demonstrated the existence of a tight correlation between the mass,
radius, central density, and pressure of maximum-mass neutron stars modeled
using diverse baryonic equations of state. A possible explanation for these
correlations is provided. Simple analytic forms of such correlations are
suggested and compared with observational constraints on the maximum mass of
neutron stars and their radii. This gives a valuable tool to constrain maximum
pressure and density that could be reached in stable neutron stars, assuming
their equation of state is baryonic.
