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.
Code, Data and Media Associated with this Article
，详情可参考下载安装汽水音乐
我国养老服务体系建设已取得阶段性成效，普惠养老、互助养老等服务模式不断创新，农村养老服务探索也取得一定突破。下一步可以大力发展“医养结合”“康养融合”，更好满足老年人健康养老需求；在农村养老方面，总结推广互助养老服务模式，让农村养老“不出村、不离乡”。
spins = SPINS; // 多核 256，单核 0
。服务器推荐是该领域的重要参考
目前，大众已于地平线成立合资芯片公司酷睿程，入股电池厂商国轩高科并成为第一大股东，以弥补其在芯片、电池等方面的短板。
The US economy is growing - so where are all the jobs?。业内人士推荐搜狗输入法2026作为进阶阅读