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The infamous strong CP problem in particle physics can in principle be solved by a massless up quark. In particular, it was hypothesized that topological effects could substantially contribute to the observed nonzero up-quark mass without reintroducing CP violation. Alternatively to previous work using fits to chiral perturbation theory, in this Letter, we bound the strength of the topological mass contribution with direct lattice QCD simulations, by computing the dependence of the pion mass ondoi:10.1103/physrevlett.125.232001 pmid:33337203 fatcat:63b7i2dlc5hlbi467iisexvlna