Three families and Pontryagin class mod 3: topological order via symmetry extension

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We show topology could help explain why quarks and leptons come in three families. Using cohomology and cobordism, we prove that a colour symmetry extension cancels a discrete Standard Model anomaly once a Pontryagin-class obstruction vanishes mod 3. The resulting Z3-gauge topological order can replace three sterile neutrinos, linking the three colours of quantum chromodynamics to three fermion generations in nature.