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We determine the $O({\ensuremath{\alpha}}_{s})$ radiative corrections to polarized top quark pair production in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations with a specified gluon energy cut. We write down fully analytical results for the unpolarized and polarized $O({\ensuremath{\alpha}}_{s})$ cross sections ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{t}t(G)$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{t}{t}^{\ensuremath{\uparrow}}(G)$ including their polar orientation dependence relative to the beam direction. In the …