  The class of effectively closed infinite-genus surfaces, defining the
completion of the domain of string perturbation theory, can be included in the
category $O_G$, which is characterized by the vanishing capacity of the ideal
boundary. The cardinality of the maximal set of endpoints is shown to be
$2^{\mit N}$. The product of the coefficient of the genus-g superstring
amplitude in four dimensions by $2^g$ in the $g\to \infty$ limit is an
exponential function of the genus with a base comparable in magnitude to the
unified gauge coupling. The value of the string coupling is consistent with the
characteristics of configurations which provide a dominant contribution to a
finite vacuum amplitude.
