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

Theorem 1.1: for a finite weakly reversible network with fixed positive rates and any positive stoichiometric class $P$ , there is a nonempty compact convex forward-invariant $K_P\subset P$ that every solution from $P$ enters in finite time; hence one $\varepsilon_P$ bounds every trajectory in $P$ between $\varepsilon_P$ and $\varepsilon_P^{-1}$ after its entry time, also on unbounded classes. The proof adds strict increase off the trapping set and a passage between scales to the companion's construction. Uniformity holds within one class and one choice of rates; entry times may depend on the initial point, and time-varying rates are not treated.

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Prior state unknown→proved

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Occurred: Oct 5, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The permanence conjecture for weakly reversible mass-action systems with fixed rates · Mass-action permanence conjecture

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Registry verification: unreviewed · announcement · candidate

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VibeMathed record: The permanence conjecture for weakly reversible mass-action systems with fixed rates

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No independent mathematician has checked this yet. Checked here: the abstract, introduction and Theorem 1.1 of the TeX source; the proof was not refereed. The family's only Lean challenge (MassAction) formalizes the companion boundedness-and-persistence theorem, whose bound depends on the initial point, so this classwise permanence statement has no formal proof at the pinned commit. The argument reuses the companion manuscript's construction, which is reproduced in the paper.

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

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

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

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

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

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