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We prove a sheaf cohomology restriction (SCORE) formula for a class of vectorbundles on complete intersections in toric varieties. The formula enables oneto compute cohomology products on the complete intersection $X$ viacomputations on the ambient space $V$ and potentially compute certain quantumcorrections to the classical sheaf cohomology ring. Schematically the formulareads $(s_1,...,s_r)_X = (s_1,...,s_r, g)_V$ with $g$ being an explicitlydescribed quantity derived from the monad data of the bundle.

A Sheaf Cohomology Restriction Formula on Toric Complete Intersections