  Building on our earlier work on toric residues and reduction, we give a proof
for the mixed toric residue conejecture of Batyrev and Materov. We simplify and
streamline our technique of tropical degenerations, which allows one to
interpolate between two localization principles: one appearing in the
intersection theory toric quotients and the other in the calculus of toric
residues. This quickly leads to the proof of the conjecture, which gives a
closed form for the summation of a generating series whose coefficients are
certain variants of the "numbers" of rational curves on toric complete
intersection Calabi-Yau manifolds.
