  The theory of stable pairs in the derived category yields an enumerative
geometry of curves in 3-folds. We evaluate the equivariant vertex for stable
pairs on toric 3-folds in terms of weighted box counting. In the toric
Calabi-Yau case, the result simplifies to a new form of pure box counting. The
conjectural equivalence with the DT vertex predicts remarkable identities. The
equivariant vertex governs primary insertions in the theory of stable pairs for
toric varieties. We consider also the descendent vertex and conjecture the
complete rationality of the descendent theory for stable pairs.
