Conserving approximations lead to thermodynamically consistent expressions for Fermi-liquid properties such as compression modulus, symmetry energy and Landau parameters. We will emphasize the need for the precision experiment to determine the density of states at the Fermi surface by discussing nuclear matter approximations in terms of thermodynamic consistency (the Hugenholtz-Van Hove theorem and the virial theorem). The density of states is the primary self-consistent observable to be determined from nuclear many-body approximations. The precise measurement of this observable will establish a rigorous criterion on the validity of nuclear matter approximations.