AgentSkillsCN

math-doc-review

审阅数学文档和证明，查找错误并生成详细、以框架为先的修正报告。当被要求审核文档中的数学命题/推导（Markdown、LaTeX、笔记本、转换为文本的PDF）时使用，并按严重程度和错误类型对问题进行分类，同时将审阅结果保存在源文件旁边的同级审阅/文件夹中。

SKILL.md
--- frontmatter
name: math-doc-review
description: Review mathematical documents and proofs to find errors and produce a detailed, framework-first correction report. Use when asked to audit math claims/derivations in docs (Markdown, LaTeX, notebooks, PDFs converted to text) and to classify issues by severity and error type, with the review saved in a sibling review/ folder next to the source file.

Math Doc Review

Overview

Provide a rigorous, framework-first review of mathematical documents, identify errors, and write a super-detailed correction report that classifies each issue by severity and error type. Treat the document's own theory and first-principles framework as the ground truth; do not import external mathematical results unless explicitly requested.

Workflow

1) Intake and scope

  • •Identify the target file(s) and scope (entire document, specific sections, or specific claims).
  • •If the framework is unclear, ask for the primary theory sources to use (definitions, axioms, permits, prior theorems). Do not proceed with external assumptions.

2) Anchor the framework

  • •Extract and list the framework anchors: definitions, axioms/permits, notational conventions, and core results the document depends on.
  • •Record these anchors in the review report so the reader can see the basis for every criticism.

3) Review pass and issue logging

  • •Read the document linearly and log potential issues with exact locations (section title, equation number, line or paragraph reference).
  • •Check each claim against the framework anchors:
    • •Are hypotheses stated and satisfied?
    • •Are parameter ranges, dimensions, and domains respected?
    • •Are definitions applied consistently?
    • •Is any step relying on an external theorem or classical analysis argument not derived in the framework?

4) Classify and analyze

  • •For each issue, assign a severity and error type using references/review-taxonomy.md.
  • •Provide a framework-first explanation of why the issue is an error or a scope restriction.
  • •Propose a concrete fix: revise statements, add missing hypotheses, or add a new lemma/permit within the framework.

5) Produce the review artifact

  • •Create a review/ folder in the same directory as the reviewed file (if it does not exist).
  • •Create the review document using assets/review-template.md and fill it in.
  • •File naming: review/<basename>.review.md where <basename> is the reviewed file name without its extension.

Output requirements

  • •Use the template and fill every section relevant to the findings.
  • •Include a severity summary and an error log table.
  • •For each error, provide step-by-step fix guidance grounded in the framework.
  • •If a claim is valid only under restricted parameters (for example, 2D only), mark it as a scope restriction and specify the exact constraint.
  • •Avoid re-proving via classical analysis; require internal permits/lemmas instead.

Resources

  • •references/review-taxonomy.md for severity levels and error-type definitions.
  • •assets/review-template.md for the report structure.