Abstract:This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.
太快了，原生计算机操作指令，是openclaw创始人入职后搞的嘛
В Москве прошла самая снежная зима14:52。PDF资料对此有专业解读
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，这一点在一键获取谷歌浏览器下载中也有详细论述
基因血脉的传递虽隐秘却坚韧，付巧妹团队通过前沿的分子生物学技术，成功提取了刻写于微小DNA片段中的信息。这项研究表明，我国西南地区藏族与南亚语族人群之间存在密切的遗传联系，而红河流域正是早期南亚语系人群迁徙和互动的枢纽之一。中华民族共同体的延续，因此增添了生物学层面的证据。
Up to 6.9x faster LLM prompt processing when compared to MacBook Pro with M1 Pro, and up to 3.9x faster than MacBook Pro with M4 Pro.，推荐阅读PDF资料获取更多信息