В Москве прошла самая снежная зима14:52
FirstFT: the day's biggest stories
Названа исполнительница роли Наташи Ростовой в «Войне и мире» Андреасяна14:45。体育直播对此有专业解读
I have 2 commits identified by their hash (Digest). I’m on the older one (bottom with the ● marker), but I can easily switch to the newer one by restarting my system (atomic method) or by using the rpm-ostree apply-live command to apply the update without restarting.，推荐阅读币安_币安注册_币安下载获取更多信息
Instead of forcing users to navigate individual retailer checkouts, companies are building agents that handle the purchasing logistics for you directly from the research phase. For example, Google has a "Buy for Me" feature that works on top of its existing price-tracking tools. Once you set your payment methods and shipping addresses, the agent will make the purchase directly on the retailer's website itself. Similarly, search-first platforms are integrating native checkouts. Perplexity features an "Instant Buy" tool that allows you to research and buy a product without ever leaving its interface. You simply fill out your details the first time, and the platform stores your information so the AI can manually make future purchases on your behalf.
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.，更多细节参见快连下载安装