  Some physical processes that occur during a star's main-sequence evolution
also affect its post main-sequence evolution. It is well known that stars with
masses above approximately 1.1 $M_{\odot}$ have well-mixed convective cores on
the main sequence, however, the structure of the star in the neighborhood of
the convective core regions is currently underconstrained. We use
asteroseismology to study the properties of the stellar core, in particular,
convective boundary mixing through convective overshoot, in such intermediate
mass stars. These core regions are poorly constrained by the acoustic (p) mode
oscillations observed for cool main sequence stars. Consequently, we seek
fossil signatures of main sequence core properties during the subgiant and
early first-ascent red giant phases of evolution. During these stages of
stellar evolution, modes of mixed character that sample the deep interior, can
be observed. These modes sample the regions of the stars that are affected by
the main-sequence structure of these regions. We model the global and near-core
properties of 62 subgiant and early first-ascent red giant branch stars
observed by the \textit{Kepler}, K2, and TESS space missions. We find that the
effective overshoot parameter, $\alpha_{\text{ov, eff}}$, increases from $M =
1.0M_{\odot}$ to $M = 1.2 M_{\odot}$ before flattening out, although we note
that the relationship between $\alpha_{\text{ov, eff}}$ and mass will depend on
the incorporated modelling choices of internal physics and nuclear reaction
network. We also situate these results within existing studies of main-sequence
convective core boundaries.
