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The transverse-target single-spin asymmetry for inclusive deep-inelastic scattering with effectively unpolarized electron and positron beams off a transversely polarized hydrogen target was measured, with the goal of searching for a two-photon exchange signal in the kinematic range 0.007 < x_B < 0.9 and 0.25 GeV2 < Q2 < 20 GeV2. In two separate regions Q2 > 1 GeV2 and Q2 < 1 GeV2, and for both electron and positron beams, the asymmetries are found to be consistent with zero within statistical and systematic uncertainties, which are of order 10(-3) for the asymmetries integrated over x_B.

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