  We sharpen the duality between open and closed topological string partition
functions for topological gravity coupled to matter. The closed string
partition function is a generalised Kontsevich matrix model in the large
dimension limit. We integrate out off-diagonal degrees of freedom associated to
one source eigenvalue, and find an open/closed topological string partition
function, thus proving open/closed duality. We match the resulting open
partition function to the generating function of intersection numbers on moduli
spaces of Riemann surfaces with boundaries and boundary insertions. Moreover,
we connect our work to the literature on a wave function of the KP integrable
hierarchy and clarify the role of the extended Virasoro generators that include
all time variables as well as the coupling to the open string observable.
