Classwise permanence for weakly reversible mass-action systems

Proves the permanence conjecture for every finite weakly reversible mass-action system with fixed positive rate constants. Every positive stoichiometric compatibility class, even an unbounded one, has a common compact convex forward-invariant absorbing set. All positive trajectories in that class therefore eventually share positive lower and finite upper concentration bounds. (Lean)

Manuscripts (2)

Uniform Permanence in Weakly Reversible Mass-Action Systems

October 5, 2026 · source · cite as \cite{OAI:Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems-October-5-2026}

We prove the permanence conjecture for finite weakly reversible mass-action systems with fixed positive reaction rates. Every positive stoichiometric compatibility class admits one compact convex forward-invariant set that every positive trajectory in that class enters in finite time, even when the class is unbounded. The set depends only on the network, the rates, and the class; the entry time may depend on the initial state. Thus, after its entry time, every concentration satisfies the same positive lower and finite upper bounds throughout that class.

Boundedness and persistence of weakly reversible mass-action systems

September 25, 2026 · source · cite as \cite{OAI:Boundedness-and-persistence-of-weakly-reversible-mass-action-systems-September-25-2026}

We prove the boundedness and persistence conjectures for finite weakly reversible mass-action systems with positive constant reaction rates. For every positive initial condition, the solution exists for all forward time, and every concentration remains bounded above and bounded away from zero. The bounds may depend on the initial condition, and no boundedness assumption is imposed on its stoichiometric compatibility class.

Result 149 · Dynamical systems and ergodic theory. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.