MMP for generalized foliated threefolds of rank one

We establish the minimal model program (MMP) for generalized foliated threefolds $(X,\mathcal{F},B,\mathbf{M})$ of rank 1, extending the result of Cascini and Spicer in [CS25d]. As an application of the generalized foliated MMP, we prove a base-point-free theorem for foliated triples on threefolds. We also prove the ACC for log canonical thresholds for generalized foliated threefolds of rank 1.