粤开证券首席经济学家罗志恒对南方周末记者解释,中国资本市场的走势主要还是“以我为主”,即上市公司质量、资本市场制度和风险偏好是关键。内部因素是长期的、根本性的,外部因素是短期的、阶段性的。
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.,更多细节参见同城约会
。体育直播是该领域的重要参考
“十五五”规划建议提出:“大力提振消费。”一个个水果新品种从“高价尝鲜”变成日常消费品,表明消费升级不只在购买力更强,也在供给侧更优。做优品质、做强品牌,让消费者在追求性价比的同时也能尝鲜选优,水果产业方能行稳致远,为美好生活增添更多甜蜜滋味。。关于这个话题,体育直播提供了深入分析
2024年12月25日 星期三 新京报
NPU仍处于早期芯片阶段,尚未被所有系统广泛采用。这项要求将使数百万PC用户无法升级到微软的下一代操作系统,但幸运的是,Windows 11的支持还将持续几年。