 This is precisely the Atiyah-Hirzebruch spectral sequence construction of twisted K-theory as a set.Diaconescu, Moore, and Witten have pointed out that the twisted K-theory classification is not compatible with the S-duality covariance of type IIB string theory.For example, consider the constraint on the Ramond–Ramond 3-form field strength G3 in the Atiyah-Hirzebruch spectral sequence (AHSS)