  NASA's Kepler Mission uncovered a wealth of planetary systems, many with
planets on short-period orbits. These short-period systems reside around 50% of
Sun-like stars and are similarly prevalent around M dwarfs. Their formation and
subsequent evolution is the subject of active debate. In this paper, we
simulate late-stage, in-situ planet formation across a grid of planetesimal
disks with varying surface density profiles and total mass. We compare
simulation results with observable characteristics of the Kepler sample. We
identify mixture models with different primordial planetesimal disk properties
that self-consistently recover the multiplicity, period ratio and duration
ratio distributions of the Kepler planets. We draw three main conclusions: (1)
We favor a "frozen-in" narrative for systems of short period planets, in which
they are stable over long timescales, as opposed to metastable. (2) The "Kepler
dichotomy", an observed phenomenon of the Kepler sample wherein the
architectures of planetary systems appear to either vary significantly or have
multiple modes, can naturally be explained by formation within planetesimal
disks with varying surface density profiles. Finally, (3) we quantify the
nature of the "Kepler dichotomy" for both GK stars and M dwarfs, and find that
it varies with stellar type. While the mode of planet formation that accounts
for highly multiplistic systems occurs in 24+/-7% of planetary systems orbiting
GK stars, it occurs in 63+/-16% of planetary systems orbiting M dwarfs.
