  The old, solar metallicity open cluster Messier 67 has long been considered a
lynchpin in the study and understanding of the structure and evolution of
solar-type stars. The same is arguably true for stellar remnants - the white
dwarf population of M67 provides crucial observational data for understanding
and interpreting white dwarf populations and evolution. In this work, we
determine the white dwarf masses and derive their progenitor star masses using
high signal-to-noise spectroscopy of warm ($\gtrsim10,000$ K) DA white dwarfs
in the cluster. From this we are able to derive each white dwarf's position on
the initial-final mass relation, with an average $M_{\mathrm WD} = 0.60\pm 0.01
M_{\odot}$ and progenitor mass $M_i = 1.52\pm 0.04 M_{\odot}$. These values are
fully consistent with recently published linear and piecewise linear fits to
the semi-empirical initial-final mass relation and provide a crucial, precise
anchor point for the initial-final mass relation for solar-metallicity,
low-mass stars. The mean mass of M67 white dwarfs is also consistent with the
sharp narrow peak in the local field white dwarf mass distribution, indicating
that a majority of recently-formed field white dwarfs come from stars with
progenitor masses of $\approx 1.5 M_{\odot}$. Our results enable more precise
modeling of the Galactic star formation rate encoded in the field WD mass
distribution.
