Natural parameter conditions for singular perturbations of chemical and biochemical reaction networks

The candidate solution reproduces the core statements of Proposition 1 and Proposition 2 for the s=1 case, using continuity on the compact set K* to control the ratio σ̂n/(σ1σn−1) (matching the paper’s Proposition 1) and a Viète-based exact identity plus an IFT expansion for the small eigenvalue to derive the ε-linear scaling of |λn/Σi<nλi| and the global chain bounds (matching the paper’s Proposition 2). The paper proves these via a different identity (Lemma 3) and obtains an O(ε) remainder term, but the hypotheses (Blanket Assumptions and Lemma 2 spectral gap) and conclusions align. A minor notational issue in the paper where ε* appears on both sides of a chain is noted by the model; reading the left bound with ε_* is consistent with Definition 2. Overall the paper’s arguments and the model’s derivation are both correct, with different but compatible proof routes .