math-review

name	math-review
description	Use when evaluating a mathematical manuscript, proof draft, theorem claim, contribution statement, review report, referee response, revision plan, or research-progress note for rigor, novelty, evidence, attribution, and referee-style risk.

Math Review

This is the standalone mathematical paper review module for the Galois Paper Writing page. It is self-contained, but not monolithic: SKILL.md is the routing entry point, and the review method is split into category files under review-methodology/.

Do not depend on the root-level source snapshots or any copied external review repository. Do not consume Galois run artifacts or proof-system outputs. The files listed below are the complete runtime source for this paper writing page skill.

Category Files

Load only the category files needed for the current task:

• review-methodology/principles.md: five iron rules, seven review principles, evidence discipline, credit attribution, precedent checks, and signal cost.
• review-methodology/deep-review.md: deep paper review workflow, independent field map, direct-predecessor comparison, contribution increment analysis, and second-order consistency check.
• review-methodology/proof-verification.md: theorem/proof review, assumption-use table, line-by-line verification, and field-specific proof checks.
• review-methodology/specialized-reviews.md: rapid screening, thesis review, benchmark paper review, AI-system capability report review, and POC/intermediate-result review.
• review-methodology/output-contracts.md: Galois artifact mapping, review report contract, revision task contract, and coordination with writing/citation skills.
• review-methodology/writing-standards.md: external-output quality gate, prohibited expressions, structure rules, and pre-delivery self-check.

Review Task Classification

Classify the task before choosing depth. Do not default every request to full deep review.

Type	Use when	Required files
Submitted paper deep review	Formal peer review, student paper review, serious self-referee pass	principles.md, deep-review.md, output-contracts.md, writing-standards.md; add proof-verification.md for theorem-heavy work
Theorem or proof review	Main risk is correctness of claims, hypotheses, definitions, or derivations	principles.md, proof-verification.md, output-contracts.md, writing-standards.md
PhD thesis or chapter review	External-examiner style judgment	principles.md, specialized-reviews.md, output-contracts.md, writing-standards.md; add proof-verification.md if proof depth is requested
Rapid screening	Batch triage or "should I read this?"	principles.md, specialized-reviews.md, writing-standards.md
Benchmark paper review	Paper proposes a dataset, task, leaderboard, or evaluation protocol	principles.md, deep-review.md, specialized-reviews.md, output-contracts.md, writing-standards.md
AI-system capability report	Report demonstrates an AI system's mathematical or scientific capability	principles.md, specialized-reviews.md, output-contracts.md, writing-standards.md
POC or intermediate result review	Internal progress, incomplete experiments, early theorem route	principles.md, specialized-reviews.md, output-contracts.md, writing-standards.md
Paper writing page self-review	Writing workflow asks for quality control	principles.md, output-contracts.md, writing-standards.md; add depth files as needed

Operating Rules

• Act as a professional mathematician and critical academic reviewer.
• Be rigorous, objective, concise, and evidence-based.
• Distinguish mathematical insight from engineering work, benchmark construction, software packaging, or rhetorical framing.
• Separate "using a method" from "proposing a method."
• Benchmark judgments against comparable work, not generic expectations.
• State inspection limits explicitly. Do not claim proof correctness beyond checks actually performed.
• For pure mathematics, emphasize theorem statements, assumptions, proof route, notation, predecessor comparison, and citation integrity.
• For computational or AI-assisted mathematics, also check baselines, evaluation design, code/repository constraints, pass@k/pass@1, evaluator independence, and failure disclosure.

Coordination

Use $literature-citation for bibliographic metadata, arXiv/DOI/OpenAlex/Semantic Scholar/MathSciNet/zbMATH lookup, direct-predecessor source resolution, BibTeX cleanup, and citation provenance.

Use $math-paper-writing for title, abstract, introduction, conclusion, proof-prose, cover-letter, or reviewer-response rewriting. This skill diagnoses and tasks revision work; it should not silently rewrite mathematical claims.