  We provide a proof for the conjectured equality of the generating function of
integrated Higgs and Coulomb branch topological operators in 3d $\mathcal{N}\ge
4$ gauge theories and the three sphere partition function deformed by mass or
FI parameters. The equality is the result of cohomological equivalence and
applies to all theories in this class, including ABJM and other generalized
Gaiotto-Witten models, and those without an explicit supersymmetric Lagrangian.
