Anthropic and Theorem Use Claude to Automatically Verify 123 Open-Source Libraries
By generating 180 million lines of mathematical proof code, the AI system identified hundreds of hidden bugs in weeks of work.
By Allison Rojas ·
Anthropic has demonstrated that its Claude AI model can automatically generate mathematical proofs to verify the safety of existing software, a process that traditionally requires years of specialized human labor. Working with partner Theorem, the team used Claude to analyze 123 open-source libraries, producing approximately 180 million lines of proof code in a matter of weeks. This achievement marks a significant shift in how software correctness is established, moving from manual inspection toward automated, mathematical validation.
The core innovation lies in the ability to translate complex software behaviors into formal mathematical problems. For decades, formal verification was reserved for high-stakes systems like aviation software because it was too expensive for general use. For instance, verifying the seL4 operating system kernel required 20 person-years of specialist work. By leveraging Claude, Anthropic’s Frontier Red Team bypassed this bottleneck, allowing the AI to handle the intensive analytical work that previously demanded extensive human expertise.
The process involves converting crash tests from Google’s OSS-Fuzz security project into mathematical queries. Claude analyzes the compiled machine code of these libraries and generates detailed proofs. An independent program called Rocq then checks these proofs for logical consistency. According to Anthropic, this workflow is nearly autonomous, requiring minimal human review, although the underlying formal foundations and tools were developed by humans at Theorem. This setup allows for a scale of verification that was previously impractical for large codebases.
Beyond just confirming safety, the system actively identified hundreds of bugs that conventional testing methods had missed. These errors often only surface under specific, rare conditions, such as unusually large input files or specific sequences of memory access. In one notable case, the team found as many security vulnerabilities in a widely used PDF reader in one week as are typically reported for that software in an entire year. In another instance, Claude detected a logical error that had remained undetected for more than a decade.
However, the term 'formally verified' carries specific technical limitations. The proofs are valid only under strict conditions, including a specific processor architecture, single-threaded execution, and input sizes under 64 MB. Since these libraries often run on diverse hardware and configurations, the verification does not guarantee error-free performance in every real-world scenario. Additionally, the computational cost is significant, with individual proofs consuming hundreds of millions of tokens, though Anthropic has not disclosed the total project costs.
The efficiency of this approach is improving rapidly. A smaller test run indicated that proofs are reusable, and newer models are becoming more efficient in their token usage. Specifically, Opus 5.5 can solve half the required proofs with approximately 40 percent fewer tokens than its predecessor, Opus 5. This trend suggests that the cost barrier to formal verification is rapidly decreasing, making it a more viable option for a broader range of software projects.
Looking ahead, Anthropic believes that AI-driven formal verification will soon become as routine as standard testing. Theorem’s roadmap already targets critical infrastructure components such as glibc, OpenSSL, and cURL. If AI can not only write code but also guarantee its correctness under defined conditions, the focus of software development will shift from basic functionality to proven safety, potentially transforming the entire landscape of automated software creation.
