The Ultimate Energy Density of Observable Cold Matter

We demonstrate that the largest measured mass of a neutron star establishes an upper bound to the energy density of observable cold matter. An equation of state-independent expression satisfied by both normal neutron stars and self-bound quark matter stars is derived for the largest energy density inside stars as a function their masses. The largest observed mass sets the lowest upper limit to the density. Implications from existing and future neutron star mass measurements are discussed.