  Let $A$ be a separable, unital, simple C*-algebra with stable rank one. We
show that every strictly positive, lower semicontinuous, affine function on the
simplex of normalized quasitraces of $A$ is realized as the rank of an operator
in the stabilization of $A$.
  Assuming moreover that $A$ has locally finite nuclear dimension, we deduce
that $A$ is $\mathcal{Z}$-stable if and only if it has strict comparison of
positive elements. In particular, the Toms-Winter conjecture holds for
separable, unital, simple, approximately subhomogeneous C*-algebras with stable
rank one.
