Formal Verification: Claude Automates Proof of 123 Libraries, Exposing Decade-Old Bugs

Formal verification has long been reserved for high-stakes systems like avionics because of its high cost. Now, Anthropic reports that its Claude model has performed this task on a large scale for existing software libraries.

The company partnered with Theorem to have Claude verify code from 123 open-source libraries in Google's OSS-Fuzz project. In a matter of weeks, the model generated approximately 180 million lines of mathematical proof code. This approach converts crash tests into mathematical problems and analyzes compiled machine code to construct proofs.

A separate verification program called Rocq checks these proofs automatically. Anthropic states that the process requires almost no human reviewers. The researchers describe the proof generation as "fully autonomous," although they note that humans at Theorem built the underlying tools and formal foundations.

Claude identified hundreds of bugs during the process and was permitted to fix them. The researchers say many of these flaws would likely have escaped conventional testing because they appear only under narrow conditions, such as unusually large input files or specific access sequences. While verifying a widely used PDF reader, the team found as many security bugs in one week as are usually reported for that software in a full year. In another case, Claude identified a logical error that had gone unnoticed for more than a decade.

Anthropic cautions that "formally verified" does not mean "error-free." The proofs hold only under specific conditions, including a particular processor architecture, single-threaded programs, and inputs smaller than 64 MB. Real-world deployments often run on different hardware and configurations.

Cost remains a constraint, as individual proofs consume hundreds of millions of tokens. Anthropic has not published total project costs. However, the company argues that if AI can verify its own code, developers can trust AI-generated software more and spend less time reviewing it. A smaller test run indicated that Opus 5.5 solves half the proofs using about 40 percent fewer tokens than Opus 5.

The project shifts the focus from whether AI can program to whether it can prove the safety of that code. Anthropic expects formal verification with AI to become as practical as standard testing. Theorem's roadmap already targets critical infrastructure, including glibc, OpenSSL, and cURL.