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The three-site Pati-Salam gauge model provides a consistent description forthe hints of lepton-flavor non-universality observed in $B$ decays, connectingthe present pattern of "anomalies" to the origin of the Standard Model Yukawacouplings. We present here a detailed analysis of the model predictions for aseries of low-energy observables, mainly in $B$ and $\tau$ physics. The modelis in good agreement with present data and predicts a well-defined pattern ofnon-standard effects in low-energy observables that could allow us to test itin the near future. Particularly interesting are the predictions of large$\tau\to\mu$ Lepton Flavor Violating processes, such as $\tau \to \mu\gamma$,$\tau \to 3\mu$, $B\to K \tau \mu$, and $B_s\to\tau\mu$. Also $\mu \to 3 e$,$\mu \to e\gamma$, and $K_L \to \mu e$ decays could be not far from the presentexclusion bounds, although this conclusion is more model dependent.

Low-energy signatures of the $\mathrm{PS}^3$ model: from $B$-physics anomalies to LFV