  We consider the colored asymmetric simple exclusion process (ASEP) and
stochastic six vertex (S6V) model with fully packed initial conditions; the
states of these models can be encoded by 2-parameter height functions. We show
under Kardar-Parisi-Zhang (KPZ) scaling of time, space, and fluctuations that
these height functions converge to the Airy sheet.
  Several corollaries follow. (1) For ASEP and the S6V model under the basic
coupling, we consider the 4-parameter height function at position $y$ and time
$t$ with a step initial condition at position $x$ and time $s < t$, and prove
that under KPZ scaling it converges to the directed landscape. (2) We prove
that ASEPs under the basic coupling, with multiple general initial data,
converge to KPZ fixed points coupled through the directed landscape. (3) We
prove that the colored ASEP stationary measures converge to the stationary
horizon. (4) We prove a strong form of decoupling for the colored ASEP height
functions, as well as for the stationary two-point function, as broadly
predicted by the theory of non-linear fluctuating hydrodynamics.
  The starting point for our Airy sheet convergence result is an embedding of
these colored models into a larger structure -- a color-indexed family of
coupled line ensembles with an explicit Gibbs property, i.e., a colored
Hall-Littlewood line ensemble. The core of our work then becomes to develop a
framework to analyze the edge scaling limit of these ensembles.
