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Over the last decade, space-born experiments have delivered new measurements of high energy cosmic-ray (CR) antiprotons and positrons, opening new frontiers in energy reach and precision. While being a promising discovery tool for new physics or exotic astrophysical phenomena, an irreducible background of antimatter comes from CR collisions with interstellar matter in the Galaxy. Understanding this irreducible source or constraining it from first principles is an interesting challenge: a game of hide-and-seek where the objective is to identify the laws of basic particle physics among the forest of astrophysical uncertainties. I describe an attempt to obtain such understanding, combining information from a zoo of CR species including massive nuclei and relativistic radioisotopes. I show that: (i) CR antiprotons most likely come from CR-gas collisions; (ii) positron data is consistent with, and suggestive of the same astrophysical production mechanism responsible for antiprotons and dominated by proton-proton collisions; (iii) the same processes produce a flux of high energy anti-helium that may be observable with a few years exposure of the AMS-02 experiment. I highlight key open questions, as well as the role played by recent and upcoming accelerator data in clarifying the origins of CR antimatter.