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We recently proposed a new experiment for precisely studying antiproton—nucleus and antideuteron—nucleus interactions at CERN’s Antiproton Decelerator. These measurements are primarily motivated by the study of (charged) cosmic rays, and in particular light antinuclei (antiprotons, antideuterons, and antihelium) that may serve as messengers for the indirect detection of particle dark matter. In this talk, I discuss the scientific motivation of the proposed measurements, a tentative experimental program, as well as the required accelerator and experiment infrastructure.