  We consider the monodromy matrix for the pure spinor IIB superstring on
$AdS_5\times S^5$ at leading order at strong coupling, in particular its
variation under an infinitesimal and continuous deformation of the contour.
Such variation is equivalent to the insertion of a local operator. Demanding
the BRST-closure for such an operator rules out its existence, implying that
the monodromy matrix remains contour-independent at the first order in
perturbation theory. Furthermore we explicitly compute the field strength
corresponding to the flat connections up to leading order and directly check
that it is free from logarithmic divergences. The absence of anomaly in the
coordinate transformation of the monodromy matrix and the UV-finiteness of the
curvature tensor finally imply the integrability of the pure spinor superstring
at the first order.
