A symmetry-extension construction of an anomalous 4d Z_{N_c}-gauge TQFT cancels the SM mixed anomaly and selects N_c = N_f = 3 as the unique odd-color solution.
Wang,Family Puzzle, Framing Topology,c − = 24and 3(E8) 1 Conformal Field Theories: 48/16 = 45/15 = 24/8 =3,arXiv:2312.14928
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Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension
A symmetry-extension construction of an anomalous 4d Z_{N_c}-gauge TQFT cancels the SM mixed anomaly and selects N_c = N_f = 3 as the unique odd-color solution.