Sign-rank preservation under constant-cost reductions

Prove that constant-cost oracle reductions preserve bounded sign-rank: given communication problems Q and P with D^Q(P) = O(1) and P of bounded sign-rank, establish that Q must also have bounded sign-rank.

Background

Sign-rank is a geometric complexity measure tightly connected to randomized communication. A general preservation theorem under constant-cost reductions would provide a powerful structural constraint on what problems can simulate others efficiently and would imply stronger separations, including those between EHD_1 and IIP_d for small d, as noted by the authors.