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.
连日来，各地区各部门各单位把开展学习教育作为重要政治任务，深入学习贯彻习近平总书记重要讲话和重要指示精神，认真落实党中央部署，精心组织实施，确保学习教育取得实效。
很不平凡的一年，镌刻很了不起的奋斗足迹。2025年，在以习近平同志为核心的党中央坚强领导下，我们迎难而上、奋力拼搏，有效应对复杂多变的国内国际形势，办了不少大事要事，顺利完成全年经济社会发展主要目标任务。我国经济顶压前行、向新向优发展，以5%的增速继续位居世界主要经济体前列，展现强大韧性和活力。人工智能、量子科技、生物医药等领域创新成果竞相涌现，我国成为创新力上升最快的经济体之一，动能和优势不断激发。从中国人民抗日战争暨世界反法西斯战争伟大胜利中汲取力量，以全球治理倡议凝聚共识，我国日益成为动荡世界中“确定性的绿洲”，彰显大国担当。。关于这个话题，51吃瓜提供了深入分析
Конфликт с Ираном вынудил США перенаправить вооружения с Украины на Ближний Восток, из-за чего Вооруженные силы страны (ВСУ) остались без критически важных систем, рассказал «Ленте.ру» военный эксперт, полковник в отставке Анатолий Матвийчук.
，推荐阅读体育直播获取更多信息
from 2002 onwards, we wanted to run BSD on Fuel, and wouldn't it be nice if，这一点在体育直播中也有详细论述
开放平台，如何转为“价值高地”？精细服务、延链补链，是破题关键。