  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 gauge
theories that can be regularized on a 3 dimensional spatial lattice when and
only when the number of flavors is an integral multiple of 16. All these
results are based on the observation that local interactions reduce the
classification 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 without
breaking any symmetry when and only when the number of boundary chiral fermions
is an integral multiple of $16$.
