proof-checker

Verify LaTeX mathematical proofs for logical gaps and invalid interchanges.

2|Updated Aug 12, 2025
One-click install
npx skills add https://github.com/goupup-ai/miccai25 --skill proof-checker-goupup-ai
Or copy as Structured Prompt for Agent
Please help me install this Agent Skill.
Skill: proof-checker
Source: https://github.com/goupup-ai/miccai25/tree/main/ARIS/skills/proof-checker
Command: npx skills add https://github.com/goupup-ai/miccai25 --skill proof-checker-goupup-ai

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Manually verifying complex mathematical proofs for logical gaps, unjustified assertions, and invalid interchanges is extremely time-consuming and error-prone, especially for high-stakes academic theory papers where small oversights can invalidate core claims.

Core Features & Use Cases

  • Cross-Model Adversarial Review: Uses a separate high-reasoning reviewer model to identify proof gaps across 20 categorized issue types, including logic errors, analysis flaws, and scope overclaims.
  • Automated Gap Fixing: Generates full derivations for identified gaps, implements fixes in LaTeX, and re-reviews until all acceptance gate criteria are met.
  • Audit Report Generation: Produces formal proof audit reports with proof-obligation accounting, counterexample red teaming results, and optional deep-fix LaTeX patches.
  • Use Case: A researcher submitting a MICCAI 2025 theory paper with complex statistical proofs can use this skill to verify all theorem steps, fix any gaps, and generate a formal audit report to strengthen the paper's validity for peer review.

Quick Start

Use the proof-checker skill to verify and fix all gaps in the LaTeX proof file located at ~/papers/miccai25/main.tex with deep-fix enabled.

Frequently Asked Questions about proof-checker

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I verify LaTeX mathematical proofs for logical gaps and unjustified assertions?

To verify LaTeX mathematical proofs for logical gaps, you can use a cross-model adversarial review process that categorizes issues like logic errors and analysis flaws. This approach rigorously audits your derivations and generates a formal proof audit trail identifying any invalid interchanges of limits, expectations, and integrals.

What is cross-model adversarial review for theorem checking?

Cross-model adversarial review for theorem checking uses a separate high-reasoning reviewer model to scrutinize your proofs. It identifies gaps across 20 categorized issue types, including scope overclaims and analysis flaws, ensuring mathematical claims withstand rigorous red teaming before academic peer review.

Can I automatically fix proof gaps and patch LaTeX files?

Yes, you can automatically fix proof gaps and patch LaTeX files using an automated gap fixing workflow. The system generates full derivations for identified gaps, implements the necessary fixes directly in LaTeX, and re-reviews the patched content until all acceptance gate criteria are met.

Does proof verification support academic theory papers in machine learning and statistics?

Yes, proof verification supports academic theory papers in machine learning, statistics, and mathematics. It rigorously checks complex statistical proofs and theorem steps, generating counterexample red teaming results and formal audit reports to strengthen paper validity for academic peer review.

What is the best way to generate a formal proof audit report with proof-obligation accounting?

The best way to generate a formal proof audit report with proof-obligation accounting is to run an automated verification workflow on your LaTeX file. This produces reproducible audit reports detailing counterexample red teaming results, categorized issue types, and optional deep-fix LaTeX patches.

Why does my mathematical proof fail due to invalid interchanges of limits and integrals?

Your mathematical proof may fail due to invalid interchanges of limits, expectations, and integrals because these operations require strict analytical conditions. An adversarial review model identifies these specific analysis flaws and generates full derivations to fix the unjustified assertions in your theorem steps.