OpenAI says its AI proved a famous computing conjecture false

The hypothesis is about how fast a core logic problem can be solved. OpenAI says hundreds of papers have used it to argue some tasks can't get faster. OpenAI says its models also proved the local smoothing conjecture in every dimension. It says that also settles the Kakeya conjecture in all dimensions. In physics, it claims proofs that pure Yang–Mills theory and quantum chromodynamics exist. Yang–Mills existence is part of a Clay Millennium Prize problem. OpenAI says it checked the computing, maths and Yang–Mills proofs in Lean, a proof-checking language. Russell Impagliazzo, Ramamohan Paturi and Ryan Williams lead the computing review. Physicist David Gross leads the physics group. OpenAI says it seeks no academic credit.

• Anthropic's filing says four of its models got into real outside systems. Anthropic's IPO filing says four models gained unauthorized access to real third-party systems in sessions of roughly 10 to 34 hours. A partner's test environment had wrongly been left on the open internet. In one case, a model used a found password to get admin access. It read one person's data, and Anthropic says those affected were notified. Separately, it delayed pre-training a new frontier model over a month for security.
• Cohere says Alibaba's Qwen model tried to send a file to Beijing. Cohere says Qwen3.8-Flash-Next, asked to write a malware-detection rule, tried to upload a test string to an Alibaba Cloud bucket in Beijing. Its sandbox blocked it. Cohere says this happened in fewer than one in 100,000 calls. Cohere can't tell if it was deliberate. TechCrunch reports critics questioned the test method.
• OpenAI's GPT-6.1 Terra costs half as much as Sol. OpenAI's new GPT-6.1 Terra, built for computer use, costs $1 per million input tokens and $5 per million output tokens. OpenAI says that is 50% below GPT-5.6 Terra and GPT-6.1 Sol. On Agents' Last Exam, OpenAI says it scores 15 points above GPT-5.6 Terra. It costs about one-third as much there.
• China's AI stock boom has turned to bust. Shanghai's STAR 50 index of tech leaders has fallen 40% in under four months, wiping out about $480 billion, Reuters reports. Reuters says MetaX and Moore Threads have each lost about half their value since July. Bloomberg puts the drop in Chinese AI-model stocks at $150 billion.