  Using a compilation of 25 studies from the literature, we investigate the
evolution of the star-forming galaxy (SFG) Main Sequence (MS) in stellar mass
and star formation rate (SFR) out to $z \sim 6$. After converting all
observations to a common set of calibrations, we find a remarkable consensus
among MS observations ($\sim 0.1$ dex 1$\sigma$ interpublication scatter). By
fitting for time evolution of the MS in bins of constant mass, we deconvolve
the observed scatter about the MS within each observed redshift bins. After
accounting for observed scatter between different SFR indicators, we find the
width of the MS distribution is $\sim 0.2$ dex and remains constant over cosmic
time. Our best fits indicate the slope of the MS is likely time-dependent, with
our best fit $\log\textrm{SFR}(M_*,t) = \left(0.84 \pm 0.02 - 0.026 \pm 0.003
\times t\right) \log M_* - \left(6.51 \pm 0.24 - 0.11 \pm 0.03 \times
t\right)$, with $t$ the age of the Universe in Gyr. We use our fits to create
empirical evolutionary tracks in order to constrain MS galaxy star formation
histories (SFHs), finding that (1) the most accurate representations of MS SFHs
are given by delayed-$\tau$ models, (2) the decline in fractional stellar mass
growth for a "typical" MS galaxy today is approximately linear for most of its
lifetime, and (3) scatter about the MS can be generated by galaxies evolving
along identical evolutionary tracks assuming an initial $1\sigma$ spread in
formation times of $\sim 1.4$ Gyr.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics