BREAKING: OpenAI’s solution to Navier–Stokes does not match its Lean verification.
The most important article to read today is not one of OpenAI’s 700 AI-generated math papers.
It is this other paper, making a deep and worrying point:
A Lean-verified proof does not automatically validate the proof written in natural language, nor does it mean that the formal statement captures the intended theorem.
During translation, an AI can change an assumption, weaken a statement, or replace the argument entirely.
It can hallucinate another theorem.
Lean correctly verifies the result.
But the proved result may no longer be what the paper claims.
This is a general problem. Things get spicy when the authors examine OpenAI’s proposed Navier–Stokes solution.
They identify at least two mismatches between the written intermediate results and their Lean counterparts:
One estimate claims that four additional input derivatives suffice. The Lean version requires five: a weaker result.
A pressure-flux estimate is obtained through a different bound, and proved through a different argument.
It is not clear whether these mismatches invalidate the entire proof.
But they raise an important issue.
OpenAI is flooding us with claimed revolutionary breakthroughs. Yet nobody knows whether the proofs are correct or whether they prove what they claim to be proving.
Epistemia at scale.
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Paper in the first reply
@donaldp1917@LouisABlanqui@eusoueumain Capital creates a material basis for which communism can be achieved through the development of productive forces. Marx makes no claim that society must develop up to a determinate point where we then transition to communism. Nor does he say that development must be capitalist.
After Kropotkin escaped from prison, he got a gig writing for the journal Nature under a fake name. One day they asked him to review Russian books on the ice age and the mountains of Asia. He had to tell the editor that he couldn't review them because he was the author, Kropotkin
aswang project is using ai… anyway if you need help researching folklore from the philippines you can start with reading through damiana eugenio’s compilations
I want to say that Aviutl now has an updated version called Aviutl 2 with English language settings!! It’s also completely free without any restrictions for tracks whatsoever 🙇♀️🙇♀️🙇♀️ I know friends who have used aviutl before shifting to ae!! And vice versa https://t.co/YDk2SvhJH0
Those are the last moments of the child Muhammad al-Zinati who had rushed to help the paramedic Sherif Shadi Lubbad, 23, who had been injured in an earlier strike. Yes, they kill children, and they kill them deliberately—again, and again, and again.
That does not prove Marx true. It refutes the claim that he was *proved* logically inconsistent. Once a coherent interpretation exists, the issue becomes which reading is textually and economically superior, not whether Marx was simply “mathematically refuted” (he wasn’t).
Dahil may nag message sa akin: Sa mga di pa nakakaalam, we gave the Cinemalaya film “Liway” away in 2022. Feel free to copy, show it for free or profit, edit, make dibidis whatever.
Eto ang link: https://t.co/F7h04GFaRe
One guy in Sweden built a search engine to fight Google, and it works.
It's called Marginalia Search.
It runs its own crawler and builds its own index instead of borrowing Bing's. It has no ads, no investors, and no loans.
What it does differently: it ranks for text-heavy, non-commercial pages. Personal blogs. Old university pages.
The weird corners SEO strangled. Every result tells you whether the page uses affiliate links and JavaScript, and you can filter them out.
There's an "explore" mode that just shows you random sites from the index. It's open source under AGPL, so you can host your own copy.
It's keyword-based, so don't type a full question at it. Type two nouns and see where you land. Every search engine now shows you the same twelve monetized pages.
This one shows you the internet people actually wrote.
https://t.co/aoaxdJk1cB
🚨 At Socialism 2026, Beatrice Adler-Bolton invokes Hamas founder Ahmed Yassin as a model for understanding disabled revolutionaries.
“Ahmed Yassin, who was an important revolutionary Palestinian leader and one of the founders and early leaders of Hamas, was paralyzed at 16. He was quadriplegic.”
She then runs through Che Guevara, Mao, Lenin, Trotsky, Ho Chi Minh, and others before concluding...
“Our debilitated, imperfect bodies are far more threatening to power than we are led to believe.”
Non ce l'ho fatta a non piangere. A dirotto.
A/I chiude.
"Ora spegnete i vostri computer, uscite di casa, lottate, abbracciatevi e continuate a sorridere. Ci fermiamo, ma la Resistenza e le idee non si fermano. Rimanete umani."
Forza, glielo dobbiamo.
https://t.co/9iHaBX1rM5
@CallaWalsh When the Trump admin and Iranian govt colluded to transfer 100+ Iranians to Iran for imprisonment, at what point exactly do they pass from being in Bad Jail to being in Good Jail? The moment they arrive in Iran? Somewhere over international waters?
https://t.co/OOdeeNy5y0
I am the screenwriter of the film RIA. I am also the partner (current girlfriend) of the director. I was made aware of a thread accusing the director of serious misconduct, part of which I was presumed to be a victim of.
The statement that the poster told about me is false.
The Partisan Defense Committee is adding Benjamin Champagne Song and other Prairieland defendants to our class-war prisoner stipend program.
Outrageously, Champagne has been sentenced to 100 years in federal prison on bogus “support to terrorism” charges for protesting at the Prairieland ICE detention facility in Texas on July 4, 2025.
The Prairieland case is the front line in the government’s war to outlaw protest. An injury to one is an injury to all! We need to fight to free all the Prairieland defendants!
As an expression of our class solidarity, the PDC has revived the tradition of the International Labor Defense by sending monthly stipends of $100 to class-war prisoners. This support for class-war prisoners is not an act of charity but the duty of those on the outside toward those inside prison walls. The PDC's other current stipend recipients are Mumia Abu-Jamal, Leonard Peltier, and Xinachtli (Alvaro Luna Hernandez).
Write letters to Benjamin Champagne Song using the following address:
Johnson County Jail, TX
Benjamin Hanil Song, 202502108
P.O. Box 247
Phoenix, MD 21131
https://t.co/2UsSNTDC7c
And follow Champagne on prison radio:
https://t.co/kvLOXCyKPN
@DFWSupCommittee