  We present a method to flexibly and self-consistently determine individual
galaxies' star formation rates (SFRs) from their host haloes' potential well
depths, assembly histories, and redshifts. The method is constrained by
galaxies' observed stellar mass functions, SFRs (specific and cosmic), quenched
fractions, UV luminosity functions, UV-SM relations, IRX-UV relations, auto-
and cross-correlation functions (including quenched and star-forming
subsamples), and quenching dependence on environment; each observable is
reproduced over the full redshift range available, up to 0<z<10. Key findings
include: galaxy assembly correlates strongly with halo assembly; quenching at
z>1 correlates strongly with halo mass; quenched fractions at fixed halo mass
decrease with increasing redshift; massive quenched galaxies reside in
higher-mass haloes than star-forming galaxies at fixed galaxy mass;
star-forming and quenched galaxies' star formation histories at fixed mass
differ most at z<0.5; satellites have large scatter in quenching timescales
after infall, and have modestly higher quenched fractions than central
galaxies; Planck cosmologies result in up to 0.3 dex lower stellar mass-halo
mass ratios at early times; and, nonetheless, stellar mass-halo mass ratios
rise at z>5. Also presented are revised stellar mass-halo mass relations for
all, quenched, star-forming, central, and satellite galaxies; the dependence of
star formation histories on halo mass, stellar mass, and galaxy SSFR; quenched
fractions and quenching timescale distributions for satellites; and predictions
for higher-redshift galaxy correlation functions and weak lensing surface
densities. The public data release (DR1) includes the massively parallel (>10^5
cores) implementation (the UniverseMachine), the newly compiled and remeasured
observational data, derived galaxy formation constraints, and mock catalogues
including lightcones.
