Ba and Clay's cyclic-cover conjecture for circular orderability, foliations, and L-spaces

Let $W$ be an irreducible rational homology $3$-sphere that is not a lens space. Ba and Clay's conjecture. The following statements are equivalent:

1. The fundamental group of $W$ is circularly orderable.
2. There exists a finite cyclic cover $\widetilde{W}$ of $W$ that supports a co-orientable taut foliation.
3. There exists a finite cyclic cover $\widetilde{W}$ of $W$ that is not an $L$-space.

This assertion links circular orderability of a rational homology sphere to foliations and the existence of non-$L$-space cyclic covers. The source presents it after proving that all closed, orientable, irreducible, toroidal $3$-manifolds are circularly orderable; it does not state that this broader assertion is proved or disproved.