SkillResearchmath

Math Research

A mathematics literature workspace. Search 9M+ theorem statements, pull citations and BibTeX from zbMATH Open, fetch full text from arXiv, no API keys. Every claim in main.tex gets a citation.

question.mdMarkdown

# Question

Write the question you want answered from the mathematical literature, then
say "go" in the chat.

Shapes that work well:

- Is it known whether ⟨statement⟩?
- What is the state of the art on ⟨problem⟩?
- Find the original source, and the best citation, for ⟨theorem⟩.
- What has been proved about ⟨object⟩ since ⟨year⟩?

The answer is written into `main.tex`, with a citation on every claim, and
`references.bib` collects the BibTeX.

main.texLaTeX

\documentclass[11pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb,amsthm}
\usepackage[numbers]{natbib}
\usepackage{hyperref}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{conjecture}[theorem]{Conjecture}

\title{Findings}
\author{}
\date{\today}

\begin{document}
\maketitle

% The agent answers question.md here, one \cite per claim.
% The example entry in references.bib shows the expected shape; replace it
% with real sources as findings land.
\nocite{*}

\bibliographystyle{plainnat}
\bibliography{references}
\end{document}

This workspace searches the mathematical literature: 9M+ theorem statements via TheoremSearch and Matlas, citation records and BibTeX via zbMATH Open, and full text via arXiv. No API keys needed. Write your question in question.md (or just ask here) and say "go": I'll answer it from the literature and write the findings into main.tex with a citation on every claim.

What’s inside

Skills

skills/arxiv/SKILL.mdarXiv · 1.8 KBUse when the question concerns results newer than late 2025 (past the semantic search corpora), when a claim must be verified against the paper's own text, or when the actual TeX source of a paper is needed (grep a proof, extract a statement verbatim). No API key.

---
name: arXiv
description: >
  Use when the question concerns results newer than late 2025 (past the
  semantic search corpora), when a claim must be verified against the
  paper's own text, or when the actual TeX source of a paper is needed
  (grep a proof, extract a statement verbatim). No API key.
---

# arXiv

Two jobs the search engines cannot do: freshness and primary-source text.

## Query API

```bash
curl -s "http://export.arxiv.org/api/query?search_query=cat:math.AG+AND+all:%22quartic%20surface%22&sortBy=submittedDate&sortOrder=descending&max_results=10"
```

Atom XML: each `<entry>` has `<id>` (the arXiv id), `<title>`,
`<summary>` (abstract), `<author>`, `<category>`, `<published>`,
`<updated>`. Useful patterns:

- `search_query=cat:math.NT+AND+all:%22...%22` scopes to a subject class.
- `id_list=2410.08415` fetches specific papers, comma-separated.
- Sort by `submittedDate` descending for "what's new on X".

Be polite: one request at a time, ~3s between requests on longer sweeps.

## Verification and full text

- **Abstract check** (the standard verification step): fetch
  `https://arxiv.org/abs/<id>` and read the abstract against the claim.
- **TeX source**: `https://arxiv.org/e-print/<id>` is a tar/gzip of the
  submission. In the sandbox:

  ```bash
  mkdir -p /tmp/arx && curl -sL https://arxiv.org/e-print/2410.08415 -o /tmp/arx/src \
    && tar -xzf /tmp/arx/src -C /tmp/arx 2>/dev/null || (cd /tmp/arx && gunzip -c src > main.tex)
  grep -rn "Cremona" /tmp/arx --include="*.tex" | head
  ```

  This is how to pull a theorem statement verbatim, check an introduction's
  history of a problem, or grep a proof for a cited lemma.
- **PDF**: `https://arxiv.org/pdf/<id>` when the source is unavailable.

Work under /tmp or .sundial/ in the sandbox: extracted paper sources are
scratch, not workspace documents.

skills/math-research/SKILL.mdMath Research · 2.5 KBUse for any nontrivial literature question in this workspace: "is this known?", "state of the art on X", "who proved this first", "survey the results on Y". The workflow that turns a question into verified, cited findings in main.tex. Read this before picking a search tool.

---
name: Math Research
description: >
  Use for any nontrivial literature question in this workspace: "is this
  known?", "state of the art on X", "who proved this first", "survey the
  results on Y". The workflow that turns a question into verified, cited
  findings in main.tex. Read this before picking a search tool.
---

# Math Research Workflow

Four stages. Skipping the verify stage is how wrong attributions end up in
print, so it is not optional.

## 1. Disambiguate

Turn the question into one or more precise mathematical statements.

- A named problem or theorem is a label, not a statement, and labels
  collide ("Gizatullin's problem" names both a Cremona-restriction problem
  for quartic surfaces and a transitivity conjecture for affine surfaces).
  Look the name up first (zbMATH search on the name, or the web) and write
  down the statement(s) it denotes.
- If the name is ambiguous, tell the user the readings you found and search
  the one(s) that fit the context, saying which you chose.

## 2. Search

- Primary: TheoremSearch (`skills/theoremsearch/SKILL.md`), querying with
  the statement, not the name. Run Matlas alongside when journal-of-record
  or textbook coverage matters.
- Metadata angle: zbMATH (`skills/zbmath/SKILL.md`) for MSC-classified
  bibliographic search and reviews.
- Freshness: the semantic corpora freeze around late 2025. For "since
  2025" questions, add an arXiv listing query
  (`skills/arxiv/SKILL.md`).

Searches are cheap; run the complementary angles rather than trusting one.

## 3. Verify

- A search hit's slogan is an LLM summary. Before citing: open the paper's
  arXiv abstract (or full text via the arxiv skill) and confirm the
  statement says what the slogan claims and is by whom the hit says.
- When two sources disagree about who proved what, the papers themselves
  are the authority: read the introductions, not more search results.
- Prefer the original source over a survey for attribution; cite the survey
  additionally when it is the better reading pointer.

## 4. Write

- Findings go into `main.tex` as normal reviewable edits, never left as
  chat output. One `\cite` per claim.
- Each cited work gets a `references.bib` entry carrying an arXiv id, DOI,
  or Zbl number (the zbmath skill covers generating BibTeX).
- Theorem statements pulled from TheoremSearch bodies are raw LaTeX; adapt
  macros to this document's preamble rather than pasting blind.
- State what was NOT found as plainly as what was: "no result on X in any
  of the four sources" is a finding.

skills/theoremsearch/SKILL.mdTheoremSearch · 2.9 KBUse when the user asks whether a mathematical result is known or proved, wants related theorems or prior work for a statement, or asks who proved something. Semantic search over 9.2M theorem statements (arXiv, Stacks Project, ProofWiki, and more), plus Matlas (180 journals back to 1826 and 1.9K textbooks) as the complement. No API key.

---
name: TheoremSearch
description: >
  Use when the user asks whether a mathematical result is known or proved,
  wants related theorems or prior work for a statement, or asks who proved
  something. Semantic search over 9.2M theorem statements (arXiv, Stacks
  Project, ProofWiki, and more), plus Matlas (180 journals back to 1826 and
  1.9K textbooks) as the complement. No API key.
---

# TheoremSearch (+ Matlas)

Theorem-level search: the results are individual statements with raw LaTeX
bodies, not just papers.

## TheoremSearch

```bash
curl -s -X POST https://api.theoremsearch.com/search \
  -H 'Content-Type: application/json' \
  -d '{"query":"every finitely generated projective module over a local ring is free","n_results":10}'
```

Request fields: `query` (required), `n_results` (default 10), `sources`,
`authors`, `types` (theorem/lemma/proposition/...), `tags`,
`year_range` ([from, to]), `citation_range`, `citation_weight` (0.0 default).

Each hit: `name` (e.g. "Theorem 2"), `body` (**raw LaTeX** of the
statement), `slogan` (an LLM-written summary), `similarity`, and `paper`
(`paper_id` like `2410.08415v3`, `title`, `link`, `primary_category`,
`year`, `journal_published`).

There is also an MCP endpoint (`https://api.theoremsearch.com/mcp`, single
`theorem_search` tool) with the same parameters.

### Query craft

- **Query with the mathematical statement, not the eponym.** The index is
  built from statement summaries, so "Gizatullin problem" ranks poorly
  while "an automorphism of a smooth quartic surface in projective
  three-space is the restriction of a Cremona transformation" hits the
  exact literature. Expand names first (see the math-research skill).
- Similarity ≥ ~0.75 hits are usually on-statement; 0.6–0.7 is
  neighborhood. Read the `body`, not just the slogan.

### Known quirks (verified live)

- `GET /paper/{paper_id}` returns 500 and `paper_filter` silently returns
  zero results. To collect all hits from one paper, search broadly and
  filter the results by `paper.paper_id` yourself.
- The corpus freezes around late 2025; `year_range: [2026, 2026]` returns
  nothing. Use the arxiv skill for anything newer.
- `slogan` is generated, `body` is source text. Cite from `body` only, and
  verify against the paper before attributing (hard rule in the addendum).

## Matlas (complement, run alongside for published/textbook coverage)

```bash
curl -s -X POST https://matlas.ai/api/search \
  -H 'Content-Type: application/json' \
  -d '{"query":"<statement>","num_results":10}'
```

Only fields: `query` and `num_results` (10–200, no other filters). Hits:
`type` (book|paper), `entity_name`, `statement`, `doi`, `title`,
`authors`, `journal`, `year`. It is the one source with textbooks (Weibel,
Scharlau, ...) and journal-of-record coverage back to 1826.

Both are academic services with undocumented rate limits: keep
`n_results` modest, and on timeout skip the source and say so rather than
retrying in a loop.

skills/zbmath/SKILL.mdzbMATH Open · 1.9 KBUse when a finding needs a citation record or BibTeX entry, when the user wants results filtered by mathematical subject (MSC class), when a named problem or theorem must be disambiguated, or when reviews of a paper would help. The bibliographic authority for mathematics: 4.8M+ records, free, no API key.

---
name: zbMATH Open
description: >
  Use when a finding needs a citation record or BibTeX entry, when the user
  wants results filtered by mathematical subject (MSC class), when a named
  problem or theorem must be disambiguated, or when reviews of a paper
  would help. The bibliographic authority for mathematics: 4.8M+ records,
  free, no API key.
---

# zbMATH Open

The mathematics equivalent of PubMed: bibliographic records with reviews,
MSC 2020 classification, DOIs, and reference lists.

## Search

```bash
curl -s "https://api.zbmath.org/v1/document/_search?search_string=projective%20module%20local%20ring&results_per_page=5&page=0"
```

The JSON lands under `result`: each record has `contributors.authors`
(`name`, plus stable author `codes`), `title`, `year`, `msc` (code +
scheme + text), `links` (DOI and others), `identifier` (the Zbl number),
`references`, and often review text.

Use it for:

- **Citation records.** The `identifier` is the Zbl number the addendum
  asks for; `links` carries the DOI.
- **Disambiguation.** Searching an eponym ("Gizatullin problem") returns
  the actual papers using the name; their titles and MSC classes reveal
  which problem is meant.
- **MSC filtering.** MSC codes in results let you separate, say, 14E07
  (birational automorphisms) from 14R (affine geometry) readings of the
  same keyword.
- **Reviews.** Review text is an expert summary of what the paper actually
  proves, often the fastest verification of an attribution short of the
  paper itself.

## BibTeX

For entries in `references.bib`, resolve the DOI through content
negotiation:

```bash
curl -sL -H "Accept: application/x-bibtex" "https://doi.org/10.2307/1995475"
```

Add the Zbl number and arXiv id (when known) to the entry's `note` field.
For arXiv-only preprints without a DOI, build the entry from the arXiv
metadata (see the arxiv skill) and cite the arXiv id.

Starter files

main.tex588 B

\documentclass[11pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb,amsthm}
\usepackage[numbers]{natbib}
\usepackage{hyperref}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{conjecture}[theorem]{Conjecture}

\title{Findings}
\author{}
\date{\today}

\begin{document}
\maketitle

% The agent answers question.md here, one \cite per claim.
% The example entry in references.bib shows the expected shape; replace it
% with real sources as findings land.
\nocite{*}

\bibliographystyle{plainnat}
\bibliography{references}
\end{document}

question.mdopens first · 467 B

# Question

Write the question you want answered from the mathematical literature, then
say "go" in the chat.

Shapes that work well:

- Is it known whether ⟨statement⟩?
- What is the state of the art on ⟨problem⟩?
- Find the original source, and the best citation, for ⟨theorem⟩.
- What has been proved about ⟨object⟩ since ⟨year⟩?

The answer is written into `main.tex`, with a citation on every claim, and
`references.bib` collects the BibTeX.

Libraries and docs

references.bib387 B

@incollection{Oguiso2013quartic,
  author    = {Oguiso, Keiji},
  title     = {Quartic {K3} surfaces and {Cremona} transformations},
  booktitle = {Arithmetic and geometry of {K3} surfaces and {Calabi--Yau} threefolds},
  series    = {Fields Inst. Commun.},
  volume    = {67},
  pages     = {455--460},
  publisher = {Springer},
  year      = {2013},
  note      = {arXiv:1110.4726},
}