  The ghost for world-sheet reparametrization invariance is not a fundamental
field in the pure spinor formalism. It is written as a combination of pure
spinor variables which have conformal dimension two and such that it commutes
with the BRST operator to give the world-sheet stress tensor. We show that the
ghost variable defined in this way is nilpotent since the OPE of b with itself
does not have singularities.
