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Now OpenAI is attempting damage control, stating that it has worked with the DOW to add new language to the contract directly addressing use of its tech for domestic surveillance.

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At capacity 1, every point gets its own cell, and the tree subdivides as deeply as possible. At capacity 10, many points coexist in the same node, and the tree stays shallow.

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.。关于这个话题,WPS下载最新地址提供了深入分析

Anthropic’

For running untrusted code in a multi-tenant environment, like short-lived scripts, AI-generated code, or customer-provided functions, you need a real boundary. gVisor gives you a user-space kernel boundary with good compatibility, while a microVM gives you a hardware boundary with the strongest guarantees. Either is defensible depending on your threat model and performance requirements.

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