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@eliqxl: никогда не прощу сценаристам смерть этой малышки id:моя брать с отметкой,scp:mу #taşacakbudeniz #yeraltı #paşa #pınar #paşnar

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Sunday 25 October 2026 21:03:18 GMT
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We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. The Millennium Prize Problems⁠ represent some of the deepest questions at the frontier of mathematics. The question of whether smooth three-dimensional fluid motion can break down has remained unresolved for roughly 90 years. A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity. To solve the Navier–Stokes problem, we used an internal model that is significantly more capable than GPT‑6 Astra. We believe it is important to inform the world about the pace of AI progress and what to expect from upcoming models. And we congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work. We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).
We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. The Millennium Prize Problems⁠ represent some of the deepest questions at the frontier of mathematics. The question of whether smooth three-dimensional fluid motion can break down has remained unresolved for roughly 90 years. A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity. To solve the Navier–Stokes problem, we used an internal model that is significantly more capable than GPT‑6 Astra. We believe it is important to inform the world about the pace of AI progress and what to expect from upcoming models. And we congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work. We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).


arrival - Isaac friend 🍂🌾🤠 #arrival #countryaesthetic #beauty #lyricedit #isaacfriend
arrival - Isaac friend 🍂🌾🤠 #arrival #countryaesthetic #beauty #lyricedit #isaacfriend
gais, bapak/ibu udah mulai jompo kayak aku? 😅 tubuh pegel, nyeri sendi, mager gerak cuma minum teh kumis kucing 2 kali sehari, beneran bisa meredahin asam urat mumpung ada, buruan coba sebelum kehabisan 🛒 cek keranjang kuning ya gais #fyp #racuntiktok #tiktokshop #asamurat #kumiskucing #solvarin
gais, bapak/ibu udah mulai jompo kayak aku? 😅 tubuh pegel, nyeri sendi, mager gerak cuma minum teh kumis kucing 2 kali sehari, beneran bisa meredahin asam urat mumpung ada, buruan coba sebelum kehabisan 🛒 cek keranjang kuning ya gais #fyp #racuntiktok #tiktokshop #asamurat #kumiskucing #solvarin
#4u #quotes #fypシ゚viral #xyzbca
#4u #quotes #fypシ゚viral #xyzbca
African mothers can turn one small mistake into a family emergency. Make dem no catch you Dey do soapy cos e no go funny lol #darktruth #psychology #deepthoughts #tiktokgrowthchallenge #darkpsychology
African mothers can turn one small mistake into a family emergency. Make dem no catch you Dey do soapy cos e no go funny lol #darktruth #psychology #deepthoughts #tiktokgrowthchallenge #darkpsychology

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