  Supernova theory has struggled to explain the lightest known neutron star
candidate with an accurate mass determination, the $1.174\mathrm{M}_\odot$
companion in the eccentric compact binary system J0453+1559. To improve the
theoretical lower limit for neutron star birth masses, we perform 3D supernova
simulations for five stellar models close to the minimum mass for iron core
collapse. We obtain a record-low neutron star mass of $1.192\mathrm{M}_\odot$
and a substantial kick of $\mathord{\sim} 100\,\mathrm{km}\,\mathrm{s}^{-1}$.
Given residual uncertainties in stellar evolution, a neutron star origin for
the $1.174\mathrm{M}_\odot$ object remains plausible.
