  The Standard Models contain chiral fermions coupled to gauge theories. It has
been a long-standing problem to give such gauged chiral fermion theories a
quantum non-perturbative definition. By classification of quantum anomalies and
symmetric invertible topological orders via a mathematical cobordism theorem
for differentiable and triangulable manifolds, and the existence of symmetric
gapped boundary for the trivial symmetric invertible topological orders, we
propose that Spin(10) chiral fermion theories with Weyl fermions in
16-dimensional spinor representations can be defined on a 3+1D lattice, and
subsequently dynamically gauged to be a Spin(10) chiral gauge theory. As a
result, the Standard Models from the 16n-chiral fermion SO(10) Grand
Unification can be defined non-perturbatively via a 3+1D local lattice model of
bosons or qubits. Furthermore, we propose that Standard Models from the
15n-chiral fermion SU(5) Grand Unification can also be realized by a 3+1D local
lattice model of fermions.
