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Abstract: Four-dimensional chiral gauge theory can be formulated as the boundary theory on a five-dimensional manifold in a manner that may be realized on a finite lattice. There are interesting features of these theories which defy a purely four-dimensional conception of universality. We find that QCD when embedded in a chiral gauge theory (the Standard Model) and regulated this way appears to suffer neither from a axial U(1) problem nor a strong CP problem, with a central role played by fermion zeromodes localized far away in the fifth dimension. In this way it differs from conventional lattice QCD formulated as a stand-alone theory. Our analysis builds on recent work by others that highlights the role of global U(1) symmetries in five dimensional formulations of four-dimensional chiral gauge theories, and the generic appearance of fermion zeromodes in the bulk.