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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 itsvariation under an infinitesimal and continuous deformation of the contour.Such variation is equivalent to the insertion of a local operator. Demandingthe BRST-closure for such an operator rules out its existence, implying thatthe monodromy matrix remains contour-independent at the first order inperturbation theory. Furthermore we explicitly compute the field strengthcorresponding to the flat connections up to leading order and directly checkthat it is free from logarithmic divergences. The absence of anomaly in thecoordinate transformation of the monodromy matrix and the UV-finiteness of thecurvature tensor finally imply the integrability of the pure spinor superstringat the first order.

Aspects of quantum integrability for pure spinor superstring in AdS(5)xS(5)