Обвинения США против Ирана описали фразой «строят самолет в процессе полета»08:51
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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Раскрыты подробности о договорных матчах в российском футболе18:01
城乡融合和区域协调发展扎实推进。年末全国常住人口城镇化率为67.89%，比上年末提高0.89个百分点。分区域看[21]，全年东部地区生产总值730876亿元，比上年增长5.0%；中部地区生产总值299108亿元，增长5.2%；西部地区生产总值298750亿元，增长5.1%；东北地区生产总值65035亿元，增长4.1%。全年京津冀地区生产总值119918亿元，比上年增长5.4%；长江经济带地区生产总值658336亿元，增长5.2%；长三角地区生产总值346595亿元，增长5.4%。粤港澳大湾区建设、黄河流域生态保护和高质量发展等区域重大战略实施取得新进展。海南自由贸易港启动全岛封关运作。（见图8）