  We study the phase diagram of (large-$N_c$) QCD using a simplistic
holographic hard-wall model with a dynamical scalar field and a homogeneous
Ansatz representing a smeared instanton/baryon density. The resulting phase
diagram is qualitatively consistent with expectations, including a mesonic,
baryonic, quarkyonic, and quark-gluon plasma phase. As in other holographic
models, we also find a baryonic popcorn transition, which appears at large
chemical potential as a crossover. We then evaluate the nuclear matter equation
of state, which turns out to be rather stiff with a large peaked sound velocity
above the conformal limit, construct corresponding neutron stars using the TOV
equations, and finally use a full numerical gravity/hydrodynamics computation
to extract the gravitational wave signal of neutron star mergers.
