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We give a conjectural but full and explicit description of the (K-theoretic)equivariant vertex for Pandharipande--Thomas stable pairs on toric Calabi--Yau4-folds, by identifying torus-fixed loci as certain quiver Grassmannians andprescribing a canonical half of the tangent-obstruction theory. For any numberof non-trivial legs, the DT/PT vertex correspondence can then be verified bycomputer in low degrees.

The 4-fold Pandharipande--Thomas vertex