number Idx to T when interpreted as Base, or Never
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.，这一点在快连下载安装中也有详细论述
。纸飞机下载对此有专业解读
“Maybe your TikTok’s taken away. But then you go on Roblox. Or you go on Discord and you start talking to people there,” he said. “That’s one of the things that is challenging…kids are super savvy, and so they’ll get around things.”。体育直播对此有专业解读
While developer Eric “ConcernedApe” Barone now has a small team to help with periodic updates, the original game – his first – was all his own work, from the distinctive pixel art and animations to the soundtrack that has since toured the world in concert. Unable to get a job after university, he’d started his own project inspired by the Harvest Moon series (now called Story of Seasons). One notable addition was the inclusion of queer romance options. The ability to pursue a romantic relationship with other townsfolk is a key part of the game’s popularity – as demonstrated by the thousands who tuned in to a video from Barone revealing the identities of two new marriage candidates – and the fact that all potential spouses are available to the player character regardless of gender has helped the game garner a dedicated queer fanbase.
The implications of sourcing-as-a-requirement are vast. What does backpropagation even look like if the weights have to be attributable, and the forward pass auditable? You won't be able to fit that in an int4, that's for sure.