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We consider theories of gauged quark flavor and identify non-invertible Peccei-Quinn symmetries arising from fractional instantons when the resulting gauge group has non-trivial global structure. Such symmetries exist solely because the Standard Model has the same numbers of generations as colors, Ng = Nc. This leads us to a massless down-type quark solution to the strong CP problem in an ultraviolet SU (9) theory of quark color-flavor unification. We show how the CKM flavor structure and weak CP violation can be generated without upsetting our solution.
Córdova et al. (Mon,) studied this question.