Proof structure
Follow dependencies from hypotheses to the main result and flag steps that do not support the claimed conclusion.
Open research tool · Codex and Claude adapters
Structured verification for mathematical papers.
UCLA Moonshot Math Verifier v.1.0 turns a broad request to “check this paper” into a structured set of independent checks, then produces a clear report for human review.
For working mathematicians, authors, and readers. Designed to assist expert review.
ILLUSTRATIVE FINDING needs review
LOCATION§4, proof of Theorem 2 · display (17)
claimed
‖T f‖q ≤ C ‖f‖p
MECHANISM
The interpolation step uses the endpoint estimate at p = 1, while the preceding lemma only establishes it for p > 1. The stated range therefore does not follow.
CORE DESIGN PRINCIPLE
The paper should be reviewed systematically across multiple passes so that errors are less likely to be missed.
Quick demonstration
See a review in practice.
Install the skill in Codex, review a local PDF, and follow a finding from the completed report to the paper and its supporting evidence.
The method
A structured workflow for checking the whole argument.
The Math Verifier skill first reads the paper as a whole, then checks it again in small sections. You can also invoke additional passes dedicated to equation checking, boundary cases, counterexample searches, or another focus you specify. A separate web-enabled pass checks cited sources. The findings are combined into a report that ranks candidate errors by severity.
- 01
Read the argument globally
Map the main claims and dependency chain, and flag outside facts for separate source checking.
- 02
Force local coverage
Partition the paper into small verification regions and audit every region line by line.
- 03
Run targeted checks
Add equation, boundary, citation, or counterexample passes where the mathematical structure calls for them.
- 04
Consolidate findings
Merge the results obtained from independent passes and generate a human-readable report.
Checks within the workflow
What the passes are organized to inspect.
A proof can fail in its global structure, a local calculation, a boundary case, or a fact imported from the literature. The workflow treats these as distinct checks.
Equations and constants
Re-derive numbered equations, signs, constants, and transitions between equations.
Quantifiers and boundaries
Check endpoints, exceptional cases, theorem scope, omitted hypotheses, and changes in quantifier order.
External obligations
Verify that each cited source supports the claimed result and that its hypotheses are satisfied when the result is applied.
A separate refuter pass can be enabled to search for small counterexamples to test central claims, as a complement to tracing the proof forward.
Finding taxonomy
How candidate errors are classified.
The class is determined by the smallest adequate repair and what that repair changes. A problem is not major merely because it appears in a central theorem.
Not repairable
Does the failure reach a central claim?
Central unsalvageable error
A central result cannot be recovered within the paper’s method.
Noncentral unsalvageable error
A secondary result fails, while the paper’s central contribution remains intact.
Repairable
What is the minimum adequate repair?
Major repairable gap
The repair needs substantive new mathematics, materially changes a principal result, or reworks multiple dependencies.
Minor repairable gap
A local correction or short addition works within the existing method and leaves the main results intact.
No mathematical change
Is the correction already forced by context?
Cosmetic or exposition only
The correction improves wording, notation, or presentation without changing the mathematical reasoning.
Overall paper verdict
Apply these rules in order to determine the recommendation.
RejectCentral unsalvageable error
Major revisionAny major repairable gap
Minor revisionNoncentral unsalvageable or minor repairable
AcceptNo mathematical gap, or cosmetic findings only
Calibration note. In human review of model-generated findings, we observed that the model can sometimes overstate an error’s severity. Severity labels should therefore be checked against the changes actually needed to fix the error.
Evidence for the design
Structured verification found more known errors than a general prompt.
In a controlled study using GPT-5.5-Sol-Ultra on 17 papers with 40 author-documented errors, two runs using required section-by-section verification found 32. Two runs using a general review prompt that left the strategy to the model found 25, while two runs using a prescribed whole-paper verification strategy found 26.
GPT-5.5-Sol-Ultra · known corrections recovered / 40
What does structured verification add?
A general prompt asks the model to find errors without requiring it to check every part of the argument. The Math Verifier skill assigns small portions of the paper to dedicated workers, instructs them to check each step, and records what they actually examined. A separate whole-paper pass checks how the argument fits together.
GENERAL PROMPT
“Read this paper and find errors.”
- No required division into small verification tasks
- No requirement to check every region individually
MATH VERIFIER SKILL
- Independent whole-paper and local verification passes
- Small paper regions checked step by step
- A record of which regions were actually checked
Team
Student researchers
- Xinjie He
- Hyunsik Chae
- Alex Taylor
- Kyle Hess
Principal investigators
- Kai-Wei Chang
- Raghu Meka
- Violet Peng
- Amit Sahai
- Terence Tao
- Wei Wang
Use the skill
One installation for app and CLI.
Set up the Math Verifier skill in Codex or Claude Code, then start with a full paper review or a focused check. The installation guide walks through setup, your first report, and the available shortcuts.
Codex · app and CLIClaude Code · desktop and CLI
A review instrument, not a verdict
Keep a mathematician in the loop.
The output is a set of candidate findings. Each one should be checked against the paper, its definitions, and—when relevant—the cited source before it is treated as an error.
Read the documentation