Motivated by the Pati-Salam Grand Unified Theory, we study (4+1)d topological insulators with SU(4) × SU(2)_1 × SU(2)_2 symmetry, whose (3+1)d boundary has 16 flavors of left-chiral fermions, which form representations (4, 2, 1) and (4̅, 1, 2). The key result we obtain is that, without any interaction, this topological insulator has a Z classification, namely any quadratic fermion mass operator at the (3+1)d boundary is prohibited by the symmetries listed above; while under interaction this

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... em becomes trivial, namely its (3+1)d boundary can be gapped out by a properly designed short range interaction without generating nonzero vacuum expectation value of any fermion bilinear mass, or in other words, its (3+1)d boundary can be driven into a "strongly coupled symmetric gapped (SCSG) phase". Based on this observation, we propose that after coupling the system to a dynamical SU(4) × SU(2)_1 × SU(2)_2 lattice gauge field, the Pati-Salam GUT can be fully regularized as the boundary states of a (4+1)d topological insulator with a thin fourth spatial dimension, the thin fourth dimension makes the entire system generically a (3+1)d system. The mirror sector on the opposite boundary will not interfere with the desired GUT, because the mirror sector is driven to the SCSG phase by a carefully designed interaction and is hence decoupled from the GUT.