OpenAI · 149-01 · 2026-10-05 · Dynamical systems and ergodic theory
Uniform Permanence in Weakly Reversible Mass-Action Systems
preprints/Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems-October-5-2026
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 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.
Preprint source and Lean scope
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A Lean scope note is stored for family 149, but it does not name this preprint. It names 149-02. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.