The circular orderability version of the L-space conjecture

Let $M$ be an irreducible, rational homology $3$-sphere that is not a lens space. Circular orderability version of the L-space conjecture. The following are equivalent:

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

This reformulation seeks to approach the L-space conjecture through finite cyclic covers. It is presented as a conjectural strengthening adapted to circular orderability, and remains open in the stated generality.