The permanence conjecture for weakly reversible mass-action systems

A mass-action system $(G,\boldsymbol{\kappa})$ has associated ODEs and is permanent if, on every compatibility class, all solutions eventually enter a compact set that remains attracting. A reaction network is weakly reversible if every reaction lies in a strongly connected component of the reaction graph. Permanence conjecture. Any weakly reversible mass-action system is permanent. Permanence is sufficient for proving the Global Attractor Conjecture for complex-balanced systems, and this conjecture proposes that it extends to the broader class of weakly reversible systems; its status is not established here.