Do we understand the star formation history of the universe?

The evolving relationship between a galaxy's mass and star formation rate -- the so-called `star-forming main sequence' (MS) -- provides a critical benchmark for understanding star formation across time. Despite its fundamental importance, the observed main sequence remains subject to substantial systematic uncertainties in normalization, shape, and redshift evolution, and a longstanding discrepancy persists between the main sequence and its integral, the stellar mass function. We revisit the star-forming MS in the era of the James Webb Space Telescope by asking what star formation rates are required by the stellar mass function to create a self-consistent picture of galaxies across time. We fit compiled ground- and space-based measurements of star-forming and quiescent mass functions from $z=0.1-9$. By tracing galaxy growth histories through these mass functions, we present a statistically-robust inference of the main sequence over $10^8 M_\odot \leq m_\star \leq 10^{11} M_\odot$, from the local universe to the first 500 Myr of cosmic history. Our procedure implies a main sequence that agrees with independent spectroscopic measurements of star formation rates from $z\sim 2-7$, is consistent with SED fitting-based analyses of photometric samples at $z\lesssim 3$, and aligns with theoretical models of galaxy evolution. However, we find that our MS differs from commonly-used `concordance' relations and thus caution against applications of these compilations without appropriately characterizing the underlying uncertainties. Finally, we explore the implications of our inferred main sequence for the galaxy-halo connection and star formation rate density, highlighting the need for further theoretical work to comprehensively understand the star formation history of the universe.