Related internet linksCare Quality Commission
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.，详情可参考heLLoword翻译官方下载
Google has improved the Pixel 10a's display, boosting its peak brightness to 3,000 nits (from 2,700). Again, a small change on paper that's more noticeable during real-world usage. Barcelona has been generous with sunshine and the occasional overcast the past few days, but I've still been able to navigate diamond-shaped streets and random passages without squinting at my phone.。关于这个话题，爱思助手提供了深入分析
Состояние зубов и десен в детстве может быть связано с риском развития сердечно-сосудистых заболеваний спустя десятилетия. К такому выводу пришли ученые из Дании, проанализировав данные более чем 568 тысяч человек. Результаты опубликованы в International Journal of Cardiology (IJC).