  Convergence of the Gauss resolution process for a complex singular foliation
of dimension r is shown to be equivalent to finite type of a graded sheaf which
is built using base (r+2) expansions of integers. As applications it is
calculated which foliations coming from split semisimple representations of
commutative Lie algebras can be resolved torically with respect to an
eigenspace decomposition and it is shown that Gaussian resolutions stabilize
for irreducible normal projective varieties with foliations of dimension r for
which (r+1)H+K is finitely generated with Iitaka dimension less than two where
H is a hyperplane section and K a canonical divisor of the foliation. For
normal irreducible complex projective varieties with very ample divisor H and a
resolvable foliation, functorial locally closed conditions on vector subspaces
X \subset |iH| are given which hold for large i and ensure that blowing up the
base locus of X and one further Gaussian blowup resolves the foliation.
