  The moduli dependence of D4-branes on a Calabi-Yau manifold is studied using
attractor flow trees, in the large volume limit of the Kahler cone. One of the
moduli dependent existence criteria of flow trees is the positivity of the flow
parameters along its edges. It is shown that the sign of the flow parameters
can be determined iteratively as function of the initial moduli, without
explicit calculation of the flow of the moduli in the tree. Using this result,
an indefinite quadratic form, which appears in the expression for the D4-D2-D0
BPS mass in the large volume limit, is proven to be positive definite for flow
trees with 3 or less endpoints. The contribution of these flow trees to the BPS
partition function is therefore convergent. From non-primitive wall-crossing is
deduced that the S-duality invariant partition function must be a generating
function of rational, multi-covering invariants instead of integer invariants.
