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.
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23:42, 3 марта 2026Россия
两者之间具有“原则—路线”相贯通的有机统一联系。在现代化进程中，有什么样的原则，就会有相应的路线。西方现代化中资本主导、个人主义、强权逻辑的原则带来殖民扩张、霸权垄断与掠夺的特征。中国式现代化以人民为中心的价值取向，将以经济建设为中心作为兴国之要，创造了后发国家实现现代化的崭新路径。习近平总书记强调：“现代化道路最终能否走得通、行得稳，关键要看是否坚持以人民为中心。”一方面，坚持以人民为中心，要求用人民主体地位和人民的全面发展统摄资本逻辑，同时积极发挥资本作为重要生产要素的生产力属性，通过市场化改革激活资本活力，助力技术创新、产业升级与就业扩容，探索出一条利用资本服务于人民的现代化之路。比如，全国工商联发布的《中国民营企业社会责任报告（2025）》显示，截至2024年底，全国共有23.51万家民营企业参与“万企兴万村”行动，产业投资额达1.23万亿元，惠及16.19万个乡村，民营企业成为服务乡村振兴战略的重要力量。另一方面，坚持以经济建设为中心，要求以内生性发展推进本国现代化，摒弃西方殖民掠夺式的现代化老路，坚定不移走和平发展道路。中国式现代化以国内超大规模市场为战略支点，通过内部产业升级与消费扩容驱动经济高质量发展，同时通过平等互惠的国际贸易与高质量共建“一带一路”合作，推动基础设施互联互通与产能合作，助力有关国家和地区实现产业升级和经济振兴。由此可见，以人民为中心与以经济建设为中心是中国式现代化价值与规律相统一的必然要求，也是中国成功走出现代化新道路的重要法宝，为后发国家实现现代化提供了可借鉴的实践范式。
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В России начали избавляться от золотаWGC: Банк России стал лидером по объемам продажи золота。关于这个话题，体育直播提供了深入分析
在外国船舶和航空器内发生的违反治安管理行为，依照中华人民共和国缔结或者参加的国际条约，中华人民共和国行使管辖权的，适用本法。