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It is well-known that three-family supersymmetric Pati-Salam models fromintersecting D6-branes, where either one or both of the ${\rm U}(2)$ gaugefactors are replaced by a ${\rm USp}(2)$ group, are quite scarce. In order toconstruct all such kind of models with generic additional gauge symmetries, wefix the observable sectors and study all the possible hidden sectors. Thus, weare able to completely determine all types of such kind of the inequivalentmodels on a $\mathbb{T}^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ orientifold fromIIA string theory. We find the gauge coupling relations to be highly sensitiveto the variations in the hidden sector. One of the models exhibits the gaugecoupling unification for a particular solution at the string scale. Inaddition, we perform scan on the hidden sector variations for the modelspresented in arXiv:2112.09632, whose gauge coupling relations are stillpreserved. Thus, we fix the gap in the previous study and complete the modelbuilding for all the inequivalent models.

The hidden sector variations in the ${\cal N}=1$ supersymmetric three-family Pati-Salam models from intersecting D6-branes