Galois

Use when drafting or revising English mathematical papers, surveys, theses, abstracts, introductions, proof prose, notation, equations, conclusions, cover letters, or reviewer responses.

Comprehensive citation management for academic research. Search Google Scholar and PubMed for papers, extract accurate metadata, validate citations, and generate properly formatted BibTeX entries. This skill should be used when you need to find papers, verify citation information, convert DOIs to BibTeX, or ensure reference accuracy in scientific writing.

Conduct comprehensive, systematic literature reviews using multiple academic databases (PubMed, arXiv, bioRxiv, Semantic Scholar, etc.). This skill should be used when conducting systematic literature reviews, meta-analyses, research synthesis, or comprehensive literature searches across biomedical, scientific, and technical domains. Creates professionally formatted markdown documents and PDFs with verified citations in multiple citation styles (APA, Nature, Vancouver, etc.).

Search 10 academic paper databases via REST APIs for research papers, preprints, and scholarly articles. Covers PubMed, PMC (full text), bioRxiv, medRxiv, arXiv, OpenAlex, Crossref, Semantic Scholar, CORE, Unpaywall. Use when searching for papers, citations, DOI/PMID lookups, abstracts, full text, open access, preprints, citation graphs, author search, or any scholarly literature query. Triggers on mentions of any supported database or requests like "find papers on X" or "look up this DOI".

Use when searching papers, organizing literature, validating citations, cleaning BibTeX, checking citation consistency, or positioning mathematical work against prior literature.

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.

Screen a decomposition plan by first trying to prove all of its subgoals directly, then identifying the key stuck points if the plan does not fully go through. Use when a decomposition plan is created.

Launch one sub-agent per decomposition plan after direct screening has identified the key stuck points for each plan. Use when all current plans have been screened by direct proving, none fully solves the problem, and parallel recursive work is needed.

Find relevant math results, constructions, examples, counterexamples, and background references for a statement. Use when you need context for a new problem, supporting references for constructing examples or counterexamples, or external results while proving subgoals.

Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second. Use when a markdown proof cites statements from external papers.

Verify a markdown proof in the order it is written. Use when the task is to check local correctness, theorem applicability, and reasoning gaps statement by statement through a paper-style proof.