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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.26094 |
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| _version_ | 1866909877999239168 |
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| author | Li, Yuxin Liu, Minghao Wang, Ruida Ji, Wenzhao He, Zhitao Pan, Rui Huang, Junming Zhang, Tong Fung, Yi R. |
| author_facet | Li, Yuxin Liu, Minghao Wang, Ruida Ji, Wenzhao He, Zhitao Pan, Rui Huang, Junming Zhang, Tong Fung, Yi R. |
| contents | We present **Lean4PHYS**, a comprehensive reasoning framework for college-level physics problems in Lean4. **Lean4PHYS** includes *LeanPhysBench*, a college-level benchmark for formal physics reasoning in Lean4, which contains 200 hand-crafted and peer-reviewed statements derived from university textbooks and physics competition problems. To establish a solid foundation for formal reasoning in physics, we also introduce *PhysLib*, a community-driven repository containing fundamental unit systems and theorems essential for formal physics reasoning. Based on the benchmark and Lean4 repository we composed in **Lean4PHYS**, we report baseline results using major expert Math Lean4 provers and state-of-the-art closed-source models, with the best performance of DeepSeek-Prover-V2-7B achieving only 16% and Claude-Sonnet-4 achieving 35%. We also conduct a detailed analysis showing that our *PhysLib* can achieve an average improvement of 11.75% in model performance. This demonstrates the challenging nature of our *LeanPhysBench* and the effectiveness of *PhysLib*. To the best of our knowledge, this is the first study to provide a physics benchmark in Lean4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lean4Physics: Comprehensive Reasoning Framework for College-level Physics in Lean4 Li, Yuxin Liu, Minghao Wang, Ruida Ji, Wenzhao He, Zhitao Pan, Rui Huang, Junming Zhang, Tong Fung, Yi R. Artificial Intelligence Machine Learning We present **Lean4PHYS**, a comprehensive reasoning framework for college-level physics problems in Lean4. **Lean4PHYS** includes *LeanPhysBench*, a college-level benchmark for formal physics reasoning in Lean4, which contains 200 hand-crafted and peer-reviewed statements derived from university textbooks and physics competition problems. To establish a solid foundation for formal reasoning in physics, we also introduce *PhysLib*, a community-driven repository containing fundamental unit systems and theorems essential for formal physics reasoning. Based on the benchmark and Lean4 repository we composed in **Lean4PHYS**, we report baseline results using major expert Math Lean4 provers and state-of-the-art closed-source models, with the best performance of DeepSeek-Prover-V2-7B achieving only 16% and Claude-Sonnet-4 achieving 35%. We also conduct a detailed analysis showing that our *PhysLib* can achieve an average improvement of 11.75% in model performance. This demonstrates the challenging nature of our *LeanPhysBench* and the effectiveness of *PhysLib*. To the best of our knowledge, this is the first study to provide a physics benchmark in Lean4. |
| title | Lean4Physics: Comprehensive Reasoning Framework for College-level Physics in Lean4 |
| topic | Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2510.26094 |