A New Census of the 0.2 < z < 3.0 Universe, Part I: The Stellar Mass
  Function
  There has been a long-standing factor-of-two tension between the observed
star formation rate density and the observed stellar mass buildup after
$z\sim2$. Recently we have proposed that sophisticated panchromatic SED models
can resolve this tension, as these methods infer systematically higher masses
and lower star formation rates than standard approaches. In a series of papers
we now extend this analysis and present a complete, self-consistent census of
galaxy formation over $0.2 < z < 3$ inferred with the \texttt{Prospector}
galaxy SED-fitting code. In this work, Paper I, we present the evolution of the
galaxy stellar mass function using new mass measurements of $\sim$10$^5$
galaxies in the 3D-HST and COSMOS-2015 surveys. We employ a new methodology to
infer the mass function from the observed stellar masses: instead of fitting
independent mass functions in a series of fixed redshift intervals, we
construct a continuity model that directly fits for the redshift evolution of
the mass function. This approach ensures a smooth picture of galaxy assembly
and makes use of the full, non-Gaussian uncertainty contours in our stellar
mass inferences. The resulting mass function has higher number densities at a
fixed stellar mass than almost any other measurement in the literature, largely
owing to the older stellar ages inferred by \texttt{Prospector}. The stellar
mass density is $\sim$50% higher than previous measurements, with the offset
peaking at $z\sim1$. The next two papers in this series will present the new
measurements of star-forming main sequence and the cosmic star formation rate
density, respectively.
