OpenAI reports classwise permanence for weakly reversible mass-action systems

For every finite weakly reversible mass-action network with fixed positive rates, each positive stoichiometric compatibility class has one compact convex forward-invariant set entered eventually by every positive trajectory in that class, including when the class is unbounded.

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Understanding the problem

Read the background

For every finite weakly reversible mass-action network with fixed positive rates, each positive stoichiometric compatibility class has one compact convex forward-invariant set entered eventually by every positive trajectory in that class, including when the class is unbounded.

Why it matters

If correct, resolves the fixed-rate permanence conjecture for weakly reversible mass-action systems.

What counts as progress

Does each positive class of a weakly reversible mass-action system have a common compact absorbing set?

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