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Star-formation rates (SFR) of disk galaxies strongly correlate with stellarmass, with a small dispersion in SSFR at fixed mass, sigma~0.3 dex. With suchsmall scatter this star-formation main sequence (SFMS) has been interpreted asdeterministic and fundamental. Here we demonstrate that it is a simpleconsequence of the central limit theorem. Our derivation begins byapproximating in situ stellar mass growth as a stochastic process, much like arandom walk (where the expectation of SFR at any time is equal to the SFR atthe previous time). We then derive expectation values for median SSFR ofstar-forming disks and their scatter over time. We generalize the results forstochastic changes in SFR that are not independent of each other but arecorrelated over time. For unbiased samples of (disk) galaxies, we derive anexpectation that <SSFR> should be independent of mass, decline as 1/T, and havea relative scatter that is independent of mass and time. The derived SFMS andits evolution matches published data to z=10 with sufficient accuracy toconstrain cosmological parameters. The framework reproduces several importantobservables, including: the scatter in SSFR at fixed mass; the SFHs of nearbydwarf galaxies and the Milky Way; and the scatter in the Tully-Fisher relation.The evolution of the mass function is less well reproduced and we discuss waysto generalize the framework to include other sources of stellar mass such asmergers. The predicted dispersion in SSFR has consequences for theclassification of quiescent galaxies, as such galaxies have heterogeneousformation histories, and many may only be temporarily diminished in theirstar-formation activity. The implied dispersion in SFHs, and the SFMS'sinsensitivity to timescales of stochasticity, thus substantially limits theability to connect massive galaxies to their progenitors over long cosmicbaselines. [TRUNC.]

Decoding the Star-Forming Main Sequence or: How I Learned to Stop Worrying and Love the Central Limit Theorem