  We describe the upper seminormal crystal structure for the $\mu$-supported
$\delta$-vectors for any quiver with potential with reachable frozen vertices,
or equivalently for the tropical points of the corresponding cluster
$\mc{X}$-variety. We show that the crystal structure can be algebraically
lifted to the generic basis of the upper cluster algebra. This can be viewed as
an additive categorification of the crystal structure arising from cluster
algebras. We introduce the biperfect bases and the strong biperfect bases in
the cluster algebra setting and give a description of all (strong) biperfect
bases, which are parametrized by lattice points in a product of explicit
polyhedral sets. We illustrate this theory from classical examples and new
examples.
