  The number of BPS bound states of D-branes on a Calabi-Yau manifold depends
on two sets of data, the BPS charges and the stability conditions. For D0 and
D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are
naturally related to the Kahler moduli space M(X). We construct unitary
one-matrix models which count such BPS states for a class of toric Calabi-Yau
manifolds at infinite 't Hooft coupling. The matrix model for the BPS counting
on X turns out to give the topological string partition function for another
Calabi-Yau manifold Y, whose Kahler moduli space M(Y) contains two copies of
M(X), one related to the BPS charges and another to the stability conditions.
The two sets of data are unified in M(Y). The matrix models have a number of
other interesting features. They compute spectral curves and mirror maps
relevant to the remodeling conjecture. For finite 't Hooft coupling they give
rise to yet more general geometry \widetilde{Y} containing Y.
