The algebraically tight contact-pair conjecture

Let $(\xi_-,\xi_+)$ be an algebraically tight contact pair on a $3$-manifold $M$, meaning that its contact invariants satisfy

$$\big\langle c(\xi_-),c(\xi_+)\big\rangle=1.$$

The algebraically tight contact-pair conjecture. The pair $(\xi_-,\xi_+)$ is homotopic through contact pairs to a positive contact pair.

The conjecture treats the contact classes as possible obstructions to deforming a tight contact pair into a positive one. The source proposes Floer-theoretic study of the coincidence locus as a possible approach and leaves the conjecture open.