therefore the following calculations will be identical.
乔忠良：从创业心态来讲，叫“流水不争先，争的是滔滔不绝”，我不喜欢大起大落，更在意企业平稳发展。第二客户哲学，叫“润物细无声”，我希望持续给客户提供价值，但不争什么，自然而然地形成扇形规模。
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.，推荐阅读谷歌浏览器【最新下载地址】获取更多信息
Standard Digital
。雷速体育对此有专业解读
MacBook Air with M5 now comes standard with 512GB of storage — double that of the previous generation — and can be configured up to 4TB for the first time, providing ample space for large projects and games. The new SSD also delivers 2x faster read/write performance compared to the previous generation, significantly accelerating file access and speeding up workflows for users, such as creators importing large photo libraries and students running AI workloads on device.5
В России ответили на имитирующие высадку на Украине учения НАТО18:04。业内人士推荐爱思助手作为进阶阅读