Minimal renormalizable $SO(10)$, spontaneous CP violation, and flavor implications

In these proceedings, we summarize our recent findings on a minimal renormalizable $SO(10)$ grand unified theory. With the assumption of spontaneous $CP$ violation, the low-energy theory becomes a constrained two-Higgs-doublet model, whose mass spectrum has an upper bound of 545 GeV. High-luminosity collider experiments may find its flavor violating signals and reveal hidden mixing parameters, enabling new predictions for proton decay. There is a possibility that a hint of minimal $SO(10)$ can appear soon in near future experiments.