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Guide · Agent skill

How to use the Proof Checker agent skill (proof-checker)

Updated · written with AI from the project's own documentation and checked against our catalogue data

The Proof Checker is an agent skill that makes a coding agent act as a rigorous reviewer of a mathematical proof written in LaTeX. It looks for gaps, fixes them with fuller derivations, re-checks the revised proof, and writes an audit log and report. This guide is for researchers, students and authors who want to use it, and it explains what you need to set up before your first run.

Proof Checkerwanshuiyin/Auto-claude-code-research-in-sleep · MIT

Quick start

  1. 1Download the ZIP. Download the proof-checker ZIP from this directory page.
  2. 2Install the skill. Unzip it into ~/.claude/skills/ for all projects, or into a project's .claude/skills/ folder, or upload it under Settings → Capabilities → Skills in the Claude apps.
  3. 3Confirm the reviewer is available. Make sure you have a Codex reviewer agent with access to the GPT-6-Astra model at ultra reasoning effort, or another reviewer backend configured in the ARIS reviewer routing.
  4. 4Make the proof available as LaTeX. Have the proof in a .tex file in your paper directory, and note its path.
  5. 5Ask for a proof check. Say something like "verify proof" or "check this proof", and give the .tex path as the argument.
  6. 6Review the findings. Open PROOF_AUDIT.md to see issues, their severity labels and the fixes applied across up to three review rounds.
  7. 7Check the acceptance status. Confirm there are no open FATAL or CRITICAL issues and note whether the semantic acceptance is provisional, then have an expert review critical results.

What is an agent skill, and what does proof-checker make the agent do?

An agent skill is a folder containing a SKILL.md file. The file tells an AI agent when a workflow applies and how to carry it out. When the skill is installed and you ask for a proof check, the agent follows the workflow in SKILL.md rather than improvising.

For proof-checker, the workflow is: read a LaTeX proof, identify gaps through a fresh-agent Codex GPT-6-Astra ultra review, fix each gap with full derivations, re-review, and generate an audit report. The skill classifies issues using a fixed taxonomy of 20 categories in four groups (logic and proof structure, analysis and measure theory, model and parameter tracking, and scope and claims). Examples of categories include UNJUSTIFIED_ASSERTION, ILLEGAL_INTERCHANGE and HIDDEN_ASSUMPTION.

  • Reads a LaTeX proof and looks for logical gaps, unjustified steps, hidden assumptions and overstated claims.
  • Writes fuller derivations to fix the issues it finds.
  • Re-reviews the revised proof for up to three rounds (MAX_REVIEW_ROUNDS = 3).
  • Produces an audit log (PROOF_AUDIT.md) and a formal before/after report (proof_audit_report.tex).

Install the proof-checker skill

Download the ZIP from this directory page. Then choose one of the two install routes below.

For Claude Code, unzip the file into your user skills folder ~/.claude/skills/, or into a project's .claude/skills/ folder if you want the skill available only in that project. For the Claude apps, upload the skill under Settings → Capabilities → Skills.

  • Option A (all projects): unzip into ~/.claude/skills/
  • Option B (one project): unzip into the project's .claude/skills/ folder
  • Option C (Claude apps): Settings → Capabilities → Skills, then upload

Check what the skill needs before you run it

The skill is not self-contained. Its base reviews are run by a Codex reviewer agent, or optionally by an Oracle MCP or other reviewer backend configured through the ARIS reviewer routing. You need access to the Codex GPT-6-Astra model at ultra reasoning effort. The allowed-tools list also names optional MCP tools (antigravity, grok, claude-review), which you only need if you configure them.

The report is a .tex file, so you need a LaTeX toolchain to compile it into a PDF. The skill runs scripts and uses the network, so review it before installing.

  • Codex reviewer agent, or an optional Oracle MCP / other reviewer backend set in the ARIS reviewer routing
  • Access to the Codex GPT-6-Astra model at ultra reasoning effort
  • Optional MCP tools (antigravity, grok, claude-review) listed in allowed-tools
  • A LaTeX toolchain for compiling the report
  • The skill runs scripts and uses the network

Trigger the skill with a natural request

You do not need a special command. The skill is triggered when you say something like the phrases listed in its description. Those include "verify proof", "proof check", "check this proof", "检查证明", "审证明", or a request for rigorous mathematical verification of a theory paper.

The skill accepts an optional argument, a path to a .tex file or a proof description, given as [path-to-tex-file or proof-description]. Point the agent at the file that contains the proof.

  • "Verify proof in paper/sections/appendix_b.tex"
  • "Proof check this lemma on convergence of the estimator"
  • "Check this proof for gaps before I submit the theory paper"

Read the output: audit log, severity labels and the acceptance gate

Each issue is scored on two axes. Axis A is proof status (INVALID, UNJUSTIFIED, UNDERSTATED, OVERSTATED or UNCLEAR). Axis B is impact (GLOBAL, LOCAL or COSMETIC). These combine into labels: FATAL, CRITICAL, MAJOR or MINOR.

The proof passes the acceptance gate only when there are zero open FATAL or CRITICAL issues, every theorem has explicit hypotheses and justified interchanges, big-O statements declare their parameter dependence, and a counterexample pass has been run on key lemmas. Results are recorded in PROOF_AUDIT.md at the paper directory root.

  • FATAL = INVALID + GLOBAL
  • CRITICAL = (INVALID + LOCAL) or (UNJUSTIFIED + GLOBAL)
  • MAJOR = (UNJUSTIFIED + LOCAL) or (UNDERSTATED/OVERSTATED + GLOBAL)
  • MINOR = clarity, notation or dimension bookkeeping that does not change claims

Understand the review independence limit

The skill labels base Codex proof judgments as same-family and provisional. A semantic proof acceptance needs a completed positive review from a reviewer with a different model family. Deterministic compilation and algebra checks can be accepted without that. If the reviewer fails, the skill emits BLOCKED rather than passing the proof.

Treat the result as a structured second check, not a certificate. The reviewer can miss subtle errors, so critical proofs still need expert human review.

What people use it for

  • Checking a theory paper's appendix proofs before submission, looking for unjustified interchanges of limits and expectations.
  • Getting a line-by-line gap check on a student's homework proof, with fuller derivations for each fix.
  • Building a documented audit trail of which steps in a proof were fixed and why, using PROOF_AUDIT.md and the compiled report.
  • Auditing a lemma for hidden assumptions, such as moment conditions or regularity that the theorem statement does not mention.
  • Spotting overstated conclusions where the claim is broader than the proof supports.

Frequently asked questions

How do I install the proof-checker skill?

Download the ZIP from this directory page and unzip it into ~/.claude/skills/ to use it everywhere, or into a project's .claude/skills/ folder to use it in one project. In the Claude apps, you can instead upload it under Settings → Capabilities → Skills.

Is the proof-checker skill free to use?

The source gives the licence as MIT. It does not state pricing for the Codex GPT-6-Astra model or other reviewer backends, so check the access terms for those services yourself.

What do I need to run proof-checker?

You need a Codex reviewer agent with access to the GPT-6-Astra model at ultra reasoning effort, or an Oracle MCP or other reviewer backend set in the ARIS reviewer routing. You also need a LaTeX toolchain to compile the report.

Can proof-checker tell me my proof is correct?

Not as a guaranteed certificate. Base reviews come from a same-family reviewer and are labelled provisional. A semantic acceptance needs a completed positive review from a different model family, and expert human review is still recommended for critical proofs.

Why did the skill say BLOCKED?

The skill emits BLOCKED when the reviewer fails. In that case the proof has not passed review, so check that your reviewer agent or backend is configured and reachable, then run the check again.

How does proof-checker compare to asking a chatbot to check a proof?

The skill uses a fixed taxonomy of 20 issue categories, two-axis severity labels, a defined acceptance gate, up to three re-review rounds and an audit log. A general chat prompt does not enforce these steps. The source does not compare it with specific other tools.

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Our verdict

Use proof-checker if you are a researcher, student or author who wants a structured, documented line-by-line check of LaTeX proofs and you can run a Codex GPT-6-Astra or other configured reviewer. Pick something else for informal or non-mathematical writing, or if you need a guaranteed correctness certificate, since its base reviews are same-family and provisional.

Download the skill