Feinberg's persistence conjecture for weakly reversible reaction systems

Let $N$ be a confined, weakly reversible mass-action ordinary differential equation system, and let $\mathfrak M^\ell(N)$ denote its associated differential inclusion. A differential inclusion is persistent when its trajectories do not approach the boundary of the nonnegative state space. Feinberg's persistence conjecture. For every confined, weakly reversible mass-action ODE system $N$, the differential inclusion $\mathfrak M^\ell(N)$ is persistent. Persistence is a central unresolved property in reaction network dynamics; the paper states that this conjecture remains open.