Comparative analysis of carbon cycle models via kinetic representations

The paper proves that for a conservative, closed network of maximal rank, ACR in some species implies co-monostationarity (Proposition 4.6). The proof argument is that two equilibria in the same co-stoichiometric class would differ by a nonzero vector in S⊥, yet ACR forces a zero in the ACR species coordinate—impossible when S⊥ is one-dimensional and spanned by a strictly positive conservation vector. The candidate solution presents the same reasoning with more explicit steps (showing S⊥ = span{v ≫ 0} and using y^1 − y^2 = αv ⇒ the i-th coordinate can’t vanish), reaching the same conclusion. This aligns directly with the paper’s statement and proof sketch of Proposition 4.6 and the definition of co-monostationarity via co-stoichiometric classes x + S⊥. See the paper’s Definition 4.5 and Proposition 4.6 for the precise statements and context: .