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Motivated by the observation that the Standard Model of particle physics(plus a right-handed neutrino) has precisely 16 Weyl fermions per generation,we search for $(3+1)$-dimensional chiral fermionic theories and chiral gaugetheories that can be regularized on a 3 dimensional spatial lattice when andonly when the number of flavors is an integral multiple of 16. All theseresults are based on the observation that local interactions reduce theclassification of certain $(4+1)$-dimensional topological superconductors from$\mathbb{Z}$ to $\mathbb{Z}_{8}$, which means that one of their$(3+1)$-dimensional boundaries can be gapped out by interactions withoutbreaking any symmetry when and only when the number of boundary chiral fermionsis an integral multiple of $16$.

Interacting Topological Superconductors and possible Origin of $16n$ Chiral Fermions in the Standard Model