How can an AI agent automatically discover security vulnerabilities in any software repository? Existing approaches use LLMs to generate software vulnerability exploits. However, it is challenging for an LLM to reliably verify its own generated exploits. In this paper, we propose Ulysses, a multi-agent security harness to synthesize verifiable vulnerability exploits for web applications. Ulysses converts candidate vulnerability findings into verified Proofs of Exploitability by iteratively exploring exploit hypotheses and establishing success in independently observed execution effects. We evaluated Ulysses on WebExploitGym, a curated benchmark of exploitable instances from 25 real-world web applications that span 5 languages and 7 frameworks. Ulysses produces verified proofs for 10 of 25 real-world advisories. It also discovered 4 new proofs of exploitability that have never been previously reported.

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