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We present the two-mass QCD contributions to the polarized pure singletoperator matrix element at three loop order in $x$-space. These terms arerelevant for calculating the polarized structure function $g_1(x,Q^2)$ at$O(\alpha_s^3)$ as well as for the matching relations in the variable flavornumber scheme and the polarized heavy quark distribution functions at the sameorder. The result for the operator matrix element is given in terms ofgeneralized iterated integrals. These integrals depend on the mass ratiothrough the main argument, and the alphabet includes square--root valuedletters.

The three-loop polarized pure singlet operator matrix element with two different masses