A graph-theoretic condition for delay stability of reaction systems

The paper’s main theorem (Theorem 5.4) establishes delay-independent stability by reducing the transcendental characteristic equation to algebraic conditions on a modified Jacobian J̃ and then using DSR-graph criteria to prove that −J̃ is a P0-matrix, together with diagonal negativity and det(−J)>0; this invokes Proposition 2.11 from prior work and Theorem 4.5/Corollary 4.6 on DSR graphs, not any positivity claim about principal minors of the characteristic matrix Δ(λ) across Re λ ≥ 0 (which the paper does not state) . The model instead asserts that all principal minors of Δ(λ) are strictly positive for all λ with Re λ ≥ 0 and concludes stability from det Δ(λ) ≠ 0. This mischaracterizes the paper’s result, treats complex minors as “positive” (not meaningful for complex values), and omits the paper’s required hypotheses (e.g., diagonal negativity from (N1) and non-singularity of J).