By 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.mdand fill it in. - File naming:
review/<basename>.review.mdwhere<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.mdfor severity levels and error-type definitions.assets/review-template.mdfor the report structure.