Autocatalytic networks and critical siphons

Let $G$ be a weakly-reversible chemical reaction network (CRN). A critical siphon is a siphon that is stoichiometrically compatible with a positive point, and $G$ is autocatalytic when it satisfies the autocatalysis conditions defined via its event-system ideal. Autocatalytic-network conjecture. $G$ is autocatalytic if and only if $G$ admits a critical siphon. The paper proves that every autocatalytic network is catalytic, while the converse characterization by critical siphons is presented as a conjecture and remains unresolved.