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Using the pure spinor formalism we prove identities which relate thetree-level, one-loop and two-loop kinematic factors for massless four-pointamplitudes. From these identities it follows that the complete supersymmetricone- and two-loop amplitudes are immediately known once the tree-levelkinematic factor is evaluated. In particular, the two-loop equivalence with theRNS formalism (up to an overall coefficient) is obtained as a corollary.

Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors