Dippolito's semi-exceptional-leaf holonomy conjecture

Let $(M,\mathcal F)$ be a codimension-one foliation of a closed manifold that is transversely $C^2$, with exceptional minimal set $\Lambda$. A semi-exceptional leaf is a boundary leaf of $M\setminus\Lambda$. Dippolito's conjecture. There exists a semi-exceptional leaf whose germs of holonomy maps form an infinite cyclic subgroup. The source presents this as a major open problem on which Dippolito's transverse-measure conjecture is conditioned.