The AMS-02 experiment has ushered cosmic-ray physics into precision era. In a companion paper, we designed an improved method to calibrate propagation models on B/C data. Here we provide a robust prediction of the $bar{p}$ flux, accounting for several sources of uncertainties and their correlations. Combined with a correlation matrix for the $bar{p}$ data, we show that the latter are consistent with a secondary origin. This paper presents key elements relevant to the dark matter search in this channel, notably by pointing out the inherent difficulties in achieving predictions at the percent-level precision.
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