Problem
Research questions and friction points this paper is trying to address.
document-level formalization
semantic auditing
mathematical formalization
proof verification
Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalization
🤖 AI Summary
This study addresses the challenges of isolated theorem processing and semantic fidelity verification in document-level mathematical formalization by proposing a human-AI collaborative end-to-end framework. Methodologically, it orchestrates the entire pipeline from specification and planning to verification, introducing an innovative evidence-based semantic auditing mechanism. This mechanism leverages large language models to construct structured evidence alongside deterministic verifiers for logical scrutiny, ensuring that formal statements faithfully reflect their informal specifications. Experimental results demonstrate that the proposed approach significantly improves both theorem proving rates and consistency detection recall. Furthermore, its practical utility is validated through the successful construction of a Lean library for numerical analysis of ordinary differential equations.
📝 Abstract
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 a direct LLM judge, both on labels verified against the source (recall 0.777 vs. 0.636) and on the original labels (0.873 vs. 0.820), and localizes each mismatch it reports to a specific hypothesis, conclusion, or scope. FYAN also built ODENumLib, a 9,355-line Lean library for the numerical analysis of ordinary differential equation.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Document-level formalization
Semantic auditing
Human-AI harness
Proof-transfer obligation
Deterministic validation
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