AI Model Produces 180 Million Lines of Proof Code in Weeks

Anthropic announced Thursday that its Claude model has generated roughly 180 million lines of mathematical proof code in just a few weeks. The effort, conducted with partner Theorem, involved verifying the safety of existing software rather than writing new code. This process aims to mathematically prove that software functions correctly under specific conditions.

Historically, proving software is error-free has been prohibitively expensive. For example, verifying the seL4 operating system kernel required 20 person-years of work by specialists. Due to this high cost, formal verification has been reserved for critical systems like Airbus avionics software. Anthropic's Frontier Red Team sought to automate this proof work using Claude.

Claude processed test programs from 123 open-source libraries found in Google's OSS-Fuzz security project. The model translated crash tests into mathematical problems and analyzed compiled machine code to generate proofs. An independent verification program called Rocq then checks these proofs. Anthropic researchers describe this process as "fully autonomous," although humans at Theorem built the underlying tools and formal foundations.

During the verification process, Claude encountered hundreds of bugs that conventional testing had missed. These bugs often only appear under specific conditions, such as unusually large input files or particular access sequences. Claude was permitted to fix these issues itself. In one instance involving a PDF reader, Claude identified as many security bugs in one week as are typically reported for that software in an entire year.

In another application, Claude detected a logical error that had persisted undetected for over a decade. Anthropic notes that even if a complete proof fails, the attempt often reveals real bugs in the code. However, the company acknowledges that "formally verified" does not mean "error-free." The proofs are only valid under strict conditions.

Specifically, the proofs assume a particular processor architecture, single-threaded programs, and inputs under 64 MB. In practice, these libraries run on various hardware and in different configurations. The compute cost for these proofs is significant, with individual proofs running up hundreds of millions of tokens. Anthropic did not report the total project costs.

If AI can verify its own code, developers may spend less time reviewing AI-generated software. Anthropic reports that newer models are becoming more efficient at this task. Its Opus 5.5 model solves half the proofs with about 40 percent fewer tokens than Opus 5. The company expects formal verification with AI will soon become as routine as standard testing.

Theorem's roadmap already targets critical infrastructure software for future verification, including glibc, OpenSSL, and cURL. If AI can write code and prove its safety under defined conditions, the implications extend beyond current coding tools. Anthropic views this capability as a major step toward software automation.