  It is known that for $K_{n,n}$ equipped with i.i.d. $exp(1)$ edge costs, the
minimum total cost of a perfect matching converges to $\pi^2/6$ in probability.
Similar convergence has been established for all edge cost distributions of
pseudo-dimension $q \geq 1$, such as Wei(1,q) costs. In this paper we extend
those results all $q>0$, confirming the M\'ezard-Parisi conjecture in the last
remaining applicable case.
