Perfect stationary solutions of reaction-diffusion equations on lattices and regular graphs

For Theorem 3.2, the paper correctly constructs a stationary solution u from any solution v of the reduced algebraic system (6), and its proof idea matches the standard row-by-row reduction argument. However, the paper’s stability “if and only if” is only justified by a brief citation to [11, Lemma 1] without stating the hypotheses or explaining how they apply here, nor clarifying that stability is meant relative to the Γ-symmetric subspace (states constant on color classes). In contrast, the model gives a complete, explicit proof: it defines the Γ-symmetric subspace, proves forward invariance, exhibits a linear isometric conjugacy between the full dynamics restricted to that subspace and the reduced ODE, and then derives the equivalence of asymptotic stability in the ℓ∞ norm on that subspace. This fills the missing steps and clarifies the correct scope of the stability claim. Stationarity agrees exactly with the paper’s construction; the stability part in the paper lacks the needed details and scope clarification, whereas the model’s treatment is precise and correct. See the statement of Theorem 3.2 and its terse proof, including the reliance on [11, Lemma 1], as given in the paper ; the definition of m-perfect coloring that underlies the reduction ; and the surrounding discussion of mergers and value–color correspondence , .