Family Unification in $SO(16)$ Grand Unification

We propose a unified model for the three Standard Model (SM) gauge symmetries and $SU(3)$ family symmetry based on $SO(16)$ grand unified gauge symmetry on six-dimensional (6D) spacetime. In this model, three chiral generations of quarks and leptons are unified into a 6D Weyl fermion in the spinor representation of $SO(16)$. The 6D $SO(16)$ gauge anomaly is canceled by the vectorlike nature of the model, and the 4D gauge anomalies are canceled by introducing suitable 4D localized fermions at the fixed point. The 4D gauge coupling constant of $SO(16)$ has the property of becoming weaker at high energies.