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We identify a new production channel for quantum chromodynamics (QCD) axions in supernova environments that contributes to axion emissivity for all models solving the strong CP problem. This channel arises at tree-level from a shift-symmetry-breaking operator constructed at next-to-leading order in chiral perturbation theory. In scenarios where model-dependent derivative couplings to nucleons are absent, this sets the strongest model-independent constraint on the axion mass, improving on existing bounds by two orders of magnitude.