  Red giants are stars in the late stages of stellar evolution. Because they
have exhausted the supply of hydrogen in their core, they burn the hydrogen in
the surrounding shell. Once the helium in the core starts fusing, the star
enters the clump phase, which is identified as a striking feature in the
color-magnitude diagram. Since clump stars share similar observational
properties, they are heavily used in astrophysical studies, as probes of
distance, extinction through the galaxy, galaxy density, and stellar chemical
evolution. In this work, we perform the detailed observational characterization
of the deepest layers of clump stars using asteroseismic data from Kepler. We
find evidence for large core structural discontinuities in about 6.7% of the
stars in our sample, implying that the region of mixing beyond the convective
core boundary has a radiative thermal stratification. These stars are otherwise
similar to the remaining stars in our sample, which may indicate that the
building of the discontinuities is an intermittent phenomenon.
