Weakly reversible reaction-system boundedness and repulsion conjecture

Let $N$ be a confined, weakly reversible reaction system, and let $\mathfrak M(N)$ denote its associated mass-action differential inclusion. Say that $\mathfrak M(N)$ is repelled by the origin when trajectories are repelled from the origin, and call a trajectory bounded when it remains in a bounded region. Boundedness and repulsion conjecture. For every confined, weakly reversible reaction system $N$, the differential inclusion $\mathfrak M(N)$ is repelled by the origin, and every trajectory of $\mathfrak M(N)$ is bounded. This assertion is presented as a reduction of the global attractor and Feinberg persistence conjectures, and the paper states that it remains open.