  We propose an explicit formula for the GW/PT descendent correspondence in the
stationary case for nonsingular projective 3-folds. The formula, written in
terms of vertex operators, is found by studying the 1-leg geometry. We prove
the proposal for all nonsingular projective toric 3-folds. An application to
the Virasoro constraints for the stationary descendent theory of stable pairs
will appear in a sequel.
