  Only one third of the nucleons in $^{208}$Pb occupy the saturation density
area. Consequently nuclear observables related to average properties of nuclei,
such as masses or radii, constrain the equation of state (EOS) not at
saturation density but rather around the so-called crossing density, localised
close to the mean value of the density of nuclei: $\rho\simeq$0.11 fm$^{-3}$.
This provides an explanation for the empirical fact that several EOS quantities
calculated with various functionals cross at a density significantly lower than
the saturation one. The third derivative M of the energy at the crossing
density is constrained by the giant monopole resonance (GMR) measurements in an
isotopic chain rather than the incompressibility at saturation density. The GMR
measurements provide M=1110 $\pm$ 70 MeV (6% uncertainty), whose extrapolation
gives K$_\infty$=230 $\pm$ 40 MeV (17% uncertainty).

Nuclear Theory