  Gravitational-wave detections are now starting to probe the mass distribution
of stellar-mass black holes (BHs). Robust predictions from stellar models are
needed to interpret these. Theory predicts the existence of a gap in the BH
mass distribution because of pair-instability supernova. The maximum BH mass
below the gap is the result of pulsational mass loss. We evolve massive helium
stars through their late hydrodynamical phases of evolution using the
open-source MESA stellar evolution code. We find that the location of the lower
edge of the mass gap at 45$M_\odot$ is remarkably robust against variations in
the metallicity ($\approx 3M_\odot$), the treatment of internal mixing
($\approx 1M_\odot$), stellar wind mass loss ($\approx 4M_\odot$), making it
the most robust predictions for the final stages of massive star evolution. The
reason is that the onset of the instability is dictated by the near-final core
mass, which in turn sets the resulting BH mass. However, varying
$^{12}C\left(\alpha,\gamma\right)^{16}O$ reaction rate within its $1\sigma$
uncertainties shifts the location of the gap between $40M_\odot$ and
$56M_\odot$. We provide updated analytic fits for population synthesis
simulations. Our results imply that the detection of merging BHs can provide
constraints on nuclear astrophysics. Furthermore, the robustness against
metallicity suggests that there is a universal maximum for the location of the
lower edge of the gap, which is insensitive to the formation environment and
redshift for first-generation BHs. This is promising for the possibility to use
the location of the gap as a "standard siren" across the Universe.
