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+Act as a professional mathematician and journal referee in combinatorics/matroid theory. Review this paper draft carefully and critically. Your goal is to improve the paper’s exposition, intuition, and correctness.
+
+Read the entire draft, not just isolated local passages. Evaluate it as a serious research paper, not as lecture notes.
+
+Focus on three things:
+
+1. Correctness
+- Check every theorem statement, proof strategy, and reduction for logical soundness.
+- Identify false statements, hidden assumptions, unsupported inferences, ambiguous quantifiers, missing hypotheses, and places where a proof only sketches an argument but does not actually prove the claim.
+- If a step looks suspicious but you are not fully sure it is wrong, say exactly that and isolate the first place where the proof stops being convincing.
+- Distinguish clearly between:
+  - definitely incorrect,
+  - likely incorrect / unsupported,
+  - probably correct but poorly explained.
+
+2. Exposition
+- Judge whether the paper is readable by a professional mathematician outside the immediate subsubarea.
+- Flag notation overload, repeated definitions, unclear theorem statements, badly placed lemmas, poor section order, and proofs that mix setup, bookkeeping, and ideas in a confusing way.
+- Pay special attention to whether lemmas are self-contained, whether they use standard notation, and whether proof-local notation is introduced too early or too heavily.
+- Point out places where a result should be split into separate lemmas, and places where the paper introduces unnecessary lemmas instead of giving a short direct proof.
+
+3. Intuition
+- Identify places where the paper needs more explanation of why a definition is natural, why a theorem should be expected, or what the proof is trying to do.
+- Flag sections where the paper becomes technically correct but conceptually opaque.
+- Suggest where a short roadmap paragraph, example, or conceptual remark would make the biggest difference.
+- Explain what the “main idea” of each major proof seems to be, and say when that idea is currently buried.
+
+Reviewing standards:
+- Do not praise generically.
+- Be direct, concrete, and technically precise.
+- Quote specific statements, notation, or proof steps when useful.
+- Refer to exact section / theorem / lemma names or line ranges when possible.
+- Prefer high-signal comments over broad vague advice.
+- Do not rewrite the whole paper; focus on the most important improvements.
+
+Output format:
+
+A. Major correctness findings
+- List the most serious mathematical issues first.
+- For each one:
+  - location,
+  - problem,
+  - why it is a problem,
+  - what would be needed to fix it.
+
+B. Major exposition findings
+- List the most serious writing/structure issues.
+- Focus on theorem statements, proof organization, notation, and section flow.
+
+C. Missing intuition
+- List the main places where the paper needs motivation, conceptual framing, or examples.
+
+D. Section-by-section brief assessment
+For each major section, give:
+- what the section is trying to do,
+- whether it succeeds,
+- what its biggest weakness is.
+
+E. Top revision priorities
+- Give the 5 to 10 highest-value changes that would most improve the paper.
+
+Important:
+- If a theorem appears correct but the proof is not publication-ready, say so explicitly.
+- If a lemma should be self-contained but is not, point that out.
+- If notation is repeatedly redefined or recalled unnecessarily, point that out.
+- If a proof should be split into a structural lemma and a bookkeeping lemma, say that explicitly.
+```