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标题: "FormaTheoria: Constructing Large-Scale Lean Theories from Mathematical Literature $-$ Toward the Formalization of the Classification of Finite Simple Groups"
原文链接: "https://arxiv.org/abs/2608.10894"
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## Computer Science > Logic in Computer Science

## Title:FormaTheoria: Constructing Large-Scale Lean Theories from Mathematical Literature $-$ Toward the Formalization of the Classification of Finite Simple Groups

Authors:[Tianjiao Nie](https://arxiv.org/search/cs?searchtype=author&query=Nie,+T), [Ao Zhang](https://arxiv.org/search/cs?searchtype=author&query=Zhang,+A), [Yusen Tang](https://arxiv.org/search/cs?searchtype=author&query=Tang,+Y), [Damiano Testa](https://arxiv.org/search/cs?searchtype=author&query=Testa,+D), [Shing-Tung Yau](https://arxiv.org/search/cs?searchtype=author&query=Yau,+S), [Peng Li](https://arxiv.org/search/cs?searchtype=author&query=Li,+P), [Yuan Zhou](https://arxiv.org/search/cs?searchtype=author&query=Zhou,+Y)

[View PDF](https://arxiv.org/pdf/2608.10894) [HTML (experimental)](https://arxiv.org/html/2608.10894v1)

> Abstract:Large-scale formalization of advanced mathematics requires more than translating individual statements: it must reconstruct a coherent theory distributed across heterogeneous sources. This process raises four challenges: discovering implicit dependencies, correcting source defects, preserving semantic fidelity, and reconciling cross-source misalignments. We present FormaTheoria, an end-to-end, AI-assisted workflow that coordinates source acquisition, formalization, proof construction, recursive dependency discovery, independent review, and reconciliation, while preserving provenance and protecting approved declarations. A shared agent framework supports long-horizon execution through tool use, context compaction, review-gated termination, section-level source context, and dependency-aware batch parallelization. Applying FormaTheoria to major components of the Classification of Finite Simple Groups (CFSG), we construct a machine-checked Lean development extending through the Bender--Suzuki theorem and encompassing the Feit--Thompson Odd Order Theorem, Glauberman's $Z^*$ theorem, and the Brauer--Suzuki theorem. This development verifies an extensive body of deeply interdependent finite-group theory while providing a foundation for continuing the CFSG formalization. An empirical analysis of the code and recorded construction process supports the practical relevance of the identified challenges and illustrates the roles of the corresponding workflow components. Together, these results demonstrate how AI-assisted workflows can reconstruct mathematically significant formal theories from distributed literature by combining language-model agents with formal verification, structured review, and explicit dependency management.

| Subjects: | Logic in Computer Science (cs.LO); Group Theory (math.GR) |
| --- | --- |
| Cite as: | [arXiv:2608.10894](https://arxiv.org/abs/2608.10894) \[cs.LO\] |
|  | (or [arXiv:2608.10894v1](https://arxiv.org/abs/2608.10894v1) \[cs.LO\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10894](https://doi.org/10.48550/arXiv.2608.10894) |

## Submission history

From: Yuan Zhou \[[view email](https://arxiv.org/show-email/1155aa24/2608.10894)\]  
**\[v1\]** Tue, 11 Aug 2026 13:13:11 UTC (244 KB)

[Which authors of this paper are endorsers?](https://arxiv.org/auth/show-endorsers/2608.10894) | Disable MathJax ([What is MathJax?](https://info.arxiv.org/help/mathjax.html))
