  Using 250 neutron star merger simulations with microphysics, we explore for
the first time the role of nuclear incompressibility in the prompt collapse
threshold for binaries with different mass ratios. We demonstrate that
observations of prompt collapse thresholds, either from binaries with two
different mass ratios or with one mass ratio but combined with the knowledge of
the maximum neutron star mass or compactness, will constrain the
incompressibility at the maximum neutron star density, $K_{\rm max}$, to within
tens of percent. This, otherwise inaccessible, measure of $K_{\rm max}$ can
potentially reveal the presence of hyperons or quarks inside neutron stars.
