[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"project-79612":3},{"id":4,"name":5,"fullName":6,"owner":7,"repo":5,"description":8,"homepage":9,"htmlUrl":10,"language":11,"languages":10,"totalLinesOfCode":10,"stars":12,"forks":13,"watchers":14,"openIssues":15,"contributorsCount":16,"subscribersCount":16,"size":16,"stars1d":15,"stars7d":17,"stars30d":18,"stars90d":16,"forks30d":16,"starsTrendScore":19,"compositeScore":20,"rankGlobal":10,"rankLanguage":10,"license":21,"archived":22,"fork":22,"defaultBranch":23,"hasWiki":22,"hasPages":24,"topics":25,"createdAt":10,"pushedAt":10,"updatedAt":26,"readmeContent":27,"aiSummary":28,"trendingCount":16,"starSnapshotCount":16,"syncStatus":29,"lastSyncTime":30,"discoverSource":31},79612,"alphaproof-nexus-results","google-deepmind\u002Falphaproof-nexus-results","google-deepmind","Lean math proofs generated by AlphaProof Nexus and accompanying natural language prose proofs.","",null,"Lean",234,19,4,1,0,78,110,11,3.9,"Apache License 2.0",false,"main",true,[],"2026-06-12 02:03:54","# AlphaProof Nexus Results\n\nThis repository contains mechanically formalized Lean proof and informal natural\nlanguage math proof results for the AlphaProof Nexus paper. The directory\nstructure is as follows:\n\n```text\n├── APNOutputs\u002F -- Lean proofs generated by AlphaProof Nexus\n│   ├── AICollaborator\u002F -- For section `Deployment in Mathematics Research`\n│   │   ├── AdditiveCombinatorics\u002F -- Additive Combinatorics\n│   │   ├── AlgebraicGeometry\u002F -- Algebraic Geometry\n│   │   ├── Graphs\u002F -- Graph Theory\n│   │   ├── Optimization\u002F -- Optimization Theory\n│   │   └── QuantumOptics\u002F -- Quantum Optics\n│   ├── ErdosProblems\u002F -- For `Erdős Problems` paragraph of `Systematic Evaluation on Open Problems`\n│   └── OEIS\u002F -- For `OEIS Problems` paragraph of `Systematic Evaluation on Open Problems`\n└── NaturalLanguageProofs\u002F -- Human-written prose proofs following the structure of the Lean proofs discovered by AlphaProof Nexus\n    ├── AICollaborator\u002F -- Proofs for subset of problems from AlphaProof Nexus \u003C-> human collaborations\n    ├── ErdosProblems\u002F -- For Erdős problems\n    └── OEIS\u002F -- Proofs for subset of OEIS problems\n```\n\nThis repository contains only problems where successful proofs were discovered by AlphaProof Nexus.\nThe [complete set of Lean problems originating from OEIS](https:\u002F\u002Fgithub.com\u002Fgoogle-deepmind\u002Fformal-conjectures\u002Ftree\u002Fauto_oeis\u002FFormalConjectures\u002FOEIS\u002FAuto) that we attempted with AlphaProof Nexus\n(including ones that were not solved) is also available, along with a\n[mapping from Lean theorem names to OEIS problems](https:\u002F\u002Fgithub.com\u002Fgoogle-deepmind\u002Fformal-conjectures\u002Fblob\u002Fauto_oeis\u002FFormalConjectures\u002FOEIS\u002FAuto\u002FTHEOREM_MAPPING.txt).\nThe complete list of Erdős problems we attempted\nis described in `erdos_problems_attempted.txt`, and Lean formalizations for these unsolved problems are available [here](https:\u002F\u002Fgithub.com\u002Fgoogle-deepmind\u002Fformal-conjectures\u002Ftree\u002Fmain\u002FFormalConjectures\u002FErdosProblems).\n\n\n## Building\n\nEnsure you have Lean 4 installed (see [installation instructions](https:\u002F\u002Flean-lang.org\u002Flean4\u002Fdoc\u002Fquickstart.html)).\n\nTo build the project and verify all proofs, run:\n\n```bash\nlake exe cache get\nlake build\n```\n\nNote that on large machines you may need to limit the parallelism of lake\nby using `LEAN_NUM_THREADS=64 lake build` or similar.\nSee [this zulip thread](https:\u002F\u002Fleanprover.zulipchat.com\u002F#narrow\u002Fchannel\u002F270676-lean4\u002Ftopic\u002FToo.20many.20open.20files.20in.20system\u002Fnear\u002F569952616).\n\n## License and disclaimer\n\nCopyright 2026 Google LLC\n\nAll software is licensed under the Apache License, Version 2.0 (Apache 2.0);\nyou may not use this file except in compliance with the Apache 2.0 license.\nYou may obtain a copy of the Apache 2.0 license at:\nhttps:\u002F\u002Fwww.apache.org\u002Flicenses\u002FLICENSE-2.0\n\nAll other materials are licensed under the Creative Commons Attribution 4.0\nInternational License (CC-BY). You may obtain a copy of the CC-BY license at:\nhttps:\u002F\u002Fcreativecommons.org\u002Flicenses\u002Fby\u002F4.0\u002Flegalcode\n\nThe content may be based on third party sources and may in some cases include\nthird party content. The original source for each conjecture is indicated by\na URL within the source file. Third party content may be subject to different\nlicensing requirements. In particular:\n\n- Material from The Online Encyclopedia of Integer Sequences available at\n  https:\u002F\u002Foeis.org and released under the Creative Commons\n  Attribution-Share-Alike License 4.0.\n- Material from Erdos Problems available at https:\u002F\u002Fwww.erdosproblems.com\u002F\n- Material provided by Gergely Berczi\n- Material provided by Mario Krenn\n\nUnless required by applicable law or agreed to in writing, all software and\nmaterials distributed here under the Apache 2.0 or CC-BY licenses are\ndistributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND,\neither express or implied. See the licenses for the specific language governing\npermissions and limitations under those licenses.\n\nThis is not an official Google product.\n","该项目提供了由AlphaProof Nexus生成的形式化Lean数学证明及其对应的自然语言描述。核心功能包括自动生成的Lean形式化证明和人工编写的自然语言证明，覆盖了加性组合、代数几何、图论、优化理论和量子光学等多个数学领域的问题。技术上采用了Lean语言，并且需要Lean 4环境来构建和验证所有证明。适用于数学研究中的自动化证明辅助以及开放问题的系统性评估场景。",2,"2026-06-11 03:58:10","CREATED_QUERY"]