Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalization

Wei Zhao, Yangshuo Zou, Chengxiang Ding, Yifan Wu, Xuchuan Wang +3

We present FYAN, a human--AI harness for document-level mathematical formalization. Rather than treating theorems in isolation, FYAN coordinates an end-to-end workflow spanning specification, proof planning, logical review, Lean proof construction, knowledge curation, and validation, with support for independent supervision and human guidance. A central component is evidence-grounded semantic auditing, which assesses whether formal statements faithfully preserve their informal specifications. A language model constructs structured evidence over local correspondences, omissions, scope, and logical relations, while a deterministic validator checks this evidence and produces reproducible judgments. When a substantive but admissible deviation is accepted, FYAN requires an explicit proof-transfer obligation connecting the formal statement back to a source-facing interpretation. With the same model (DeepSeek-V4.1-Flash) in every stage, FYAN proves 86 of 143 FormalTCS theorems under a strict Lean check, against 69 for a general agent harness, and raises the natural-language proof score from 0.501 to 0.851. On ConsistencyCheck, its semantic audit catches more inconsistent statements than…