2501.06354
From chemical reaction networks to algebraic and polyhedral geometry – and back again
Elisenda Feliu, Anne Shiu
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper states the theorem that minimal siphons are exactly the inclusion-minimal sets {i : xi ∈ P} among minimal primes P of TG (with TG defined in Q[x]/⟨x1⋯xn⟩) and cites [SS10] for details; no proof is given in the survey text. The candidate solution supplies a complete, rigorous proof by working in Q[x] with I := ⟨x^yi(x^yj − x^yi)⟩ + ⟨x1⋯xn⟩, using the quotient–prime correspondence and standard prime-ideal arguments. This matches the paper’s stated result (Theorem 3.3) but constitutes an explicit proof not present in the survey itself .
Referee report (LaTeX)
\textbf{Recommendation:} no revision
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The survey accurately states the siphon–prime correspondence and situates it within the broader context of persistence and boundary steady states. The candidate’s proof is standard, complete, and aligns with the statement. Given the survey nature of the paper, the absence of a detailed proof is acceptable; the exposition, examples, and references are adequate.