Independent, Incidence Independent and Weakly Reversible Decompositions of Chemical Reaction Networks

Bryan S. Hernandez, Deza A. Amistas, Ralph John L. De la Cruz, Lauro L. Fontanil, Aurelio A. de los Reyes V, Eduardo R. Mendoza

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Proposition 4.2 states exactly the claim: for a weakly reversible network N, any incidence independent decomposition N = N1 ∪ ... ∪ Nk is weakly reversible. Its proof sketches that weak reversibility gives a positive vector in Ker Ia; incidence independence then forces a positive vector in Ker Ia,i for each subnetwork, which is equivalent to weak reversibility of each Ni . The candidate solution provides the same core argument but with two explicit details: (i) it constructs a strictly positive circulation in Ker Ia by summing cycle flows, and (ii) it proves the equivalence “positive vector in Ker Ia > 0 ⇒ weakly reversible” via a condensation-DAG argument, which the paper treats as standard folklore. Logically, both are correct and essentially the same proof, differing only in the level of detail. Definitions of the incidence map and incidence independence used in both align with the paper’s preliminaries .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The audited proposition is correct and contributes a clean, practically useful bridge from an algebraic decomposition criterion (incidence independence) to weak reversibility of all subnetworks. The proof is standard and sound. A minor enhancement would be to cite or briefly justify the equivalence between weak reversibility and the existence of a positive vector in the kernel of the incidence map, which is invoked as folklore. Otherwise, the exposition is clear and consistent with CRNT foundations.