The boundedness and persistence conjectures for weakly reversible mass-action systems

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The boundedness and persistence conjectures for weakly reversible mass-action systems parent of this event

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Theorem 1.1: for any finite weakly reversible network with positive constant rates and any positive $x^0$, the solution exists for all $t\ge0$ and some $\varepsilon\in(0,1)$, depending on the network, the rates and $x^0$, gives $\varepsilon\le x_i(t)\le\varepsilon^{-1}$ for all $t\ge0$ and all $i$. The proof builds a compact convex forward-invariant polytope around each initial point from a finite concave piecewise-affine function. A remark derives convergence for complex-balanced systems, which the paper treats as known (citing Craciun's 2026 revision), not as new. The bounds are not uniform over a compatibility class (the permanence entry), and time-dependent rates are not treated. parent of this event

Companion: Boundedness and persistence of weakly reversible mass-action systems (input to this proof) evidence for this event

VibeMathed record: The boundedness and persistence conjectures for weakly reversible mass-action systems evidence for this event

Lean: OAI/Analysis/MassAction/Main.lean (global_bounded_persistent_solution) evidence for this event

The permanence conjecture for weakly reversible mass-action systems with fixed rates evidence for this event

Anderson, Boundedness of trajectories for weakly reversible, single linkage class reaction systems (arXiv:1104.4992) evidence for this event