New Agent Pipeline Audits Formalized Numerical Analysis Beyond Kernel Acceptance.

Recent advancements in coding agents have shown their capability to formalize complex mathematical texts. This new work extends these efforts by applying a coding agent to formalize numerical analysis, a field largely absent from current formal mathematics libraries like Mathlib. The agent demonstrates the ability to develop new theoretical formalizations from the ground up. A significant contribution is a novel, systematic framework for assessing the quality of agent-generated formalizations. This framework goes beyond simply checking if the code compiles, evaluating semantic correctness, reuse of existing Mathlib components, and cross-file reuse using an LLM-as-judge approach. Applying this evaluation method revealed recurring issues in formalizations, such as incomplete statements and added hypotheses, which are not caught by traditional compilation-based metrics. The findings suggest that current success metrics might overstate the true quality of autoformalization systems, advocating for more rigorous audit methodologies.