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Building on our recent proposal to explain the experimental hints of new physics in $B$ meson decays within the framework of Pati-Salam quark-lepton unification, through the interactions of the $(3,1)_{2/3}$ vector leptoquark, we construct a realistic model of this type based on the gauge group ${\rm SU}(4)_L \times {\rm SU}(4)_R \times {\rm SU}(2)_L \times {\rm U}(1)'$ and consistent with all experimental constraints.
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