Computationally Checking if a Reaction Network is Monotone or Non-expansive

The paper’s equivalence (Theorem 2) between monotonicity/non-expansiveness and closure under operations 1–3 is correct and well supported by its decomposition J_f = ∑ Γ_i ∂R_i, the cross-positivity criterion, and a reduction to single-reaction checks plus known lifting arguments for norms. The model’s argument for (A) (monotonicity with respect to a cone) aligns with the paper and is essentially correct. However, its converse proof for (B) (non-expansiveness with respect to a norm) contains a critical gap: it concludes q − αΓ_i ∈ B from the fact that this point lies in all supporting half-spaces at the single boundary point q. That local half-space containment does not imply global membership in B, so the model’s (B)⇐ direction is invalid without additional structure (e.g., a lifting proof or a global support characterization), which the paper provides via prior results. Hence, overall: paper correct, model wrong.