The Persistence Conjecture for weakly reversible mass action systems

A mass action system is a chemical reaction network whose reaction rates follow the mass action law. A reaction network is weakly reversible when every reaction belongs to a directed cycle in the reaction graph. A system is persistent when every trajectory starting in the positive orthant avoids convergence to the boundary, so no initially present species tends toward extinction.

Persistence Conjecture. Every weakly reversible mass action system is persistent.

This conjecture would imply the Global Attractor Conjecture as a corollary and motivated geometric approaches based on reaction vectors pointing away from boundary faces. The source attributes the original conjecture to Martin Feinberg and its current formulation to Gheorghe Craciun and collaborators; its resolution is not established by the supplied evidence.