«Я не верю Зеленскому. Даже в то, что у него нос между глазами». В Европе пошли на противостояние с Зеленским из-за «Дружбы»08:50
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.
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Then the pandemic brought new problems, even though at first it brought enormous growth—revenue rose nearly 20% in 2020. But keeping up with that demand overwhelmed the company. Target lost sight of what set it apart from the likes of Walmart, Ulta Beauty, and Amazon. It didn’t help that Target later backed away from years of pledged support for diversity and inclusion efforts that aimed for higher representation of minority groups in the company and among suppliers, and then clumsily flip-flopped on its showcasing of merchandise tied to events like LGBTQ Pride month under pressure from right-wing activists, angering consumers across the political spectrum.
arXivLabs: experimental projects with community collaborators