Tech firms will have 48 hours to remove abusive images under new law
AI 手机的道路，不会只有「孤勇者」
。体育直播是该领域的重要参考
2026-02-22 21:04:33 +01:00
В России предупредили о скорой нехватке вагонов08:46。体育直播对此有专业解读
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.
The cabin crew had just served breakfast when Dzafran Azmir felt the first tremor. He and the other two hundred and ten passengers on Singapore Airlines Flight SQ321 had been in the air for more than ten hours. Their flight had taken off the night before from the United Kingdom, where Azmir was studying audio engineering at the University of Plymouth, and had flown across Central Europe, the Black Sea, Turkmenistan, and Pakistan. They were thirty-seven thousand feet above the Irrawaddy River, in Myanmar—three hours from their scheduled landing in Singapore—when the turbulence started. For a moment, the plane quivered around them like a greyhound straining on a leash. Then it lifted its nose and leaped forward on an updraft. Eleven seconds later—at 7:49:32 A.M. on May 21, 2024, according to the flight’s data recorder—the pilots switched on the “Fasten Seat Belt” sign and told the flight attendants to secure the cabin. They were in for some rough weather.。关于这个话题，体育直播提供了深入分析