Claude generates massive proofs to verify code safety

Software developers have long struggled to guarantee that their code is safe. Traditional testing finds many errors, but it rarely proves that a program will never fail under every possible condition. That gap leaves room for critical bugs to slip through. Now, a new approach is closing that gap by using artificial intelligence to do the heavy lifting of mathematical verification.

Anthropic and its partner Theorem used the Claude model to mathematically verify existing software. The team focused on 123 open-source libraries from Google's OSS-Fuzz security project. Instead of writing new code, Claude analyzed compiled machine code and translated crash tests into mathematical problems. The model generated roughly 180 million lines of proof code in just a few weeks.

This method is not new, but it has always been expensive and slow. In the past, formal verification required teams of specialists. For example, verifying the small operating system kernel seL4 took 20 person-years. Because of that cost, the method was mostly reserved for high-stakes systems like avionics software. The new AI-driven process changes the economics of the task.

An independent program called Rocq checks the proofs generated by Claude. According to Anthropic, the process requires very little human review. The researchers describe it as fully autonomous, though humans built the underlying tools and formal foundations. This automation allows for a scale of verification that was previously impossible for most software projects.

The project uncovered hundreds of bugs that conventional testing had missed. Many of these errors only appear under specific conditions, such as unusually large input files or particular access sequences. Claude was allowed to fix these bugs itself. In one instance, the team found as many security bugs in a widely used PDF reader in one week as are typically reported in an entire year.

Claude also caught a logical error that had gone undetected for over a decade. Even when a complete proof fails, the attempt still surfaces real issues. This suggests that the verification process has value beyond just certifying safety. It acts as a powerful debugging tool that finds deep, hidden flaws in complex software.

However, the term formally verified does not mean error-free. The proofs only hold under strict conditions, such as a specific processor architecture and inputs under 64 MB. Real-world software often runs on different hardware and configurations. The compute cost is also steep, with individual proofs consuming hundreds of millions of tokens. Anthropic did not report the total cost of the project.

Newer models are making the process more efficient. Opus 5.5 solves half the proofs with about 40 percent fewer tokens than Opus 5. This trend points to a future where AI can verify its own code more cheaply. If developers can trust AI-generated software more, they can spend less time on manual review. That saves costs across the entire development process.

The project strengthens the case for software automation. The question is no longer whether AI can program, but whether it can prove that its code is safe. Anthropic expects this method to become as routine as standard testing. Theorem's roadmap already targets critical infrastructure like glibc, OpenSSL, and cURL. This shift could have consequences that go well beyond current coding tools.