  We present the first catalogs of the highest-energy (above 56 TeV and 100
TeV) gamma-ray sources seen by the High Altitude Water Cherenkov (HAWC)
Observatory. The wide field-of-view of HAWC naturally lends itself to unbiased
all-sky surveys and newly developed event-by-event gamma-ray energy
reconstruction algorithms have allowed unprecedented energy resolution. The
sources presented here are the highest-energy sources ever detected. All are
coincident with known lower-energy gamma-ray sources within our Galaxy. These
objects may have implications for the sources of Galactic cosmic rays; since
Galactic CRs have been observed up to PeV energies, sources accelerating
particles to these energies must exist. These sources, called "PeVatrons",
would have corresponding hard gamma-ray spectra that extend to high energies
without any spectral break or cutoff. We will present measurements of the
spectra of these highest-energy gamma-ray sources and discuss if any of them
can be identified as PeVatron candidates.
