OpenAI · 149-02 · 2026-09-25 · Dynamical systems and ergodic theory
Boundedness and persistence of weakly reversible mass-action systems
preprints/Boundedness-and-persistence-of-weakly-reversible-mass-action-systems-September-25-2026
Family 149. Permanence for weakly reversible reaction networks.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
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.
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.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 149: Classwise permanence for weakly reversible mass-action systems. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.