  Using the first 50% of data collected for the Spitzer Large Area Survey with
Hyper-Suprime-Cam (SPLASH) observations on the 1.8 deg$^2$ Cosmological
Evolution Survey (COSMOS) we estimate the masses and star formation rates of
3398 $M_*>10^{10}M_\odot $ star-forming galaxies at $4 < z < 6$ with a
substantial population up to $M_* \gtrsim 10^{11.5} M_\odot$. We find that the
strong correlation between stellar mass and star formation rate seen at lower
redshift (the "main sequence" of star-forming galaxies) extends to $z\sim6$.
The observed relation and scatter is consistent with a continued increase in
star formation rate at fixed mass in line with extrapolations from
lower-redshift observations. It is difficult to explain this continued
correlation, especially for the most massive systems, unless the most massive
galaxies are forming stars near their Eddington-limited rate from their first
collapse. Furthermore, we find no evidence for moderate quenching at higher
masses, indicating quenching either has not occurred prior to $z \sim 6$ or
else occurs rapidly, so that few galaxies are visible in transition between
star-forming and quenched.
