  We give bijections between bipolar-oriented (acyclic with unique source and
sink) planar maps and certain random walks, which show that the uniformly
random bipolar-oriented planar map, decorated by the "peano curve" surrounding
the tree of left-most paths to the sink, converges in law with respect to the
peanosphere topology to a $\sqrt{4/3}$-Liouville quantum gravity surface
decorated by an independent Schramm-Loewner evolution with parameter
$\kappa=12$ (i.e., SLE$_{12}$). This result is universal in the sense that it
holds for bipolar-oriented triangulations, quadrangulations, $k$-angulations,
and maps in which face sizes are mixed.
