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Abstract 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 1.1M_⊙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 parts 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 theKepler, K2, and TESS space missions. We find that the effective overshoot parameter,α_ov,eff, increases fromM= 1.0M_⊙toM= 1.2M_⊙before flattening out, although we note that the relationship betweenα_ov,effand mass will depend on the incorporated modeling choices of internal physics and nuclear reaction network. We also situate these results within existing studies of main-sequence convective core boundaries.