  We analyze the population statistics of black holes in the LIGO/Virgo/KAGRA
GWTC-3 catalog using a parametric mass function derived from simulations of
massive stars experiencing pulsational pair-instability supernovae (PPISN). Our
formalism enables us to separate the black hole mass function into
sub-populations corresponding to mergers between objects formed via different
astrophysical pathways, allowing us to infer the properties of black holes
formed from stellar collapse and black holes formed via prior mergers
separately. Applying this formalism, we find that this model fits the data
better than the powerlaw+peak model with Bayes factor $ 9.7\pm0.1$. We measure
the location of the lower edge of the upper black hole mass gap to be $M_{\rm
BHMG}=84.05_{-12.88}^{+17.19}{\rm M}_{\odot}$, providing evidence that the
$35{\rm M}_{\odot}$ Gaussian peak detected in the data using other models is
not associated with the PPISN pile-up predicted to precede this gap.
Incorporating spin, we find that the normalized spins of stellar remnant black
holes are close to zero while those of higher generation black holes tend to
larger values. All of these results are in accordance with the predictions of
stellar structure theory and black hole merger scenarios. Finally, we combine
our mass function with the spectral siren method for measuring the Hubble
constant to find $H_0=36.19_{-10.91}^{17.50}$ km/s/Mpc and discuss potential
explanations of this low value. Our results demonstrate how
astrophysically-informed mass functions can facilitate the interpretation of
gravitational wave catalog data to provide information about black hole
formation and cosmology. Future data releases will improve the precision of our
measurements.
