An AI-assisted proof of a 1988 conjecture, and Beijing's reply

Christian Coester, Elias Koutsoupias and Marek Zbysiński posted a proof on Monday of the k-server conjecture, a central open question in online algorithms that Mark Manasse, Lyle McGeoch and Daniel Sleator posed in 1988 and that the field has long called its holy grail. The paper spells out who did what. The authors proved the three-server case without AI and refined their approach in discussions with ChatGPT and Gemini. OpenAI's GPT-6 Astra then derived the proof for any number of servers, which the authors adapted and revised. The result has not yet been peer reviewed.

Beijing answered the frontier labs' call to slow AI development on Monday. Foreign Ministry spokesperson Guo Jiakun said fear-mongering and malicious competition would only disrupt global AI governance, and the state-run Global Times called the proposal a Cold War playbook packed with provisions aimed at China. The two capitals now read the same essay in opposite ways. Speaking by phone to Nvidia's Jensen Huang onstage at the All-In Summit, President Trump called the slowdown push a hoax that plays into the hands of people who could include China. China's State Security Minister, Chen Yixin, separately urged faster construction of a national system for preventing AI security risks.

Microsoft AI released a 37-page draft Humanist AI Code of Conduct for its own models and opened it to public comment for six weeks. Its absolute constraints bar help with cyberattacks, nuclear weapons and deepfakes, and its control rules forbid a model from evading oversight so that it can no longer be directed or shut down. The code also states that AI is not conscious and should not imitate consciousness, and it rejects legal personhood and model welfare, a direct break with the model welfare research Anthropic has pursued. Microsoft is not training on the draft yet and plans to use a revised version from 2027.

Apple shipped iOS 27 and its sister updates on Monday, bringing Siri AI to compatible devices as an opt-in beta in English, with French, Japanese, Korean, Portuguese and Spanish due in October. The rebuilt assistant reads personal context across messages, email and photos and can act inside apps. Apple's release notes say features that run on its servers, Siri AI among them, carry daily usage limits, and that expanded access will be sold for a fee later. Some users may need to join a waitlist first. Apple builds the underlying models itself, using Google's Gemini in their development.

OpenAI has bought Glass Imaging, a Los Altos startup founded by former Apple engineers Ziv Attar and Tom Bishop, who led the team behind the iPhone's Portrait Mode, according to The Wall Street Journal. The reported price is more than $300 million. Neither company has confirmed it. Glass Imaging trains a neural network for each individual camera module, replacing the usual chain of separate image-processing steps, and its software already ships in Honor phones. The deal adds camera expertise to OpenAI's consumer hardware effort, which began with its purchase of Jony Ive's io.

The I3LUNG project, a study across six centers in Italy, Germany, Greece, Israel, Spain and the United States, reported in Nature Medicine that AI models built from 2,396 patients with advanced non-small cell lung cancer predicted immunotherapy outcomes better than every standard clinical biomarker, including the PD-L1 test doctors rely on. When 20 physicians reviewed 100 real cases with the tool, their accuracy in spotting responders rose substantially, with the largest gains among doctors who were not lung cancer specialists. This phase looked back at past patients; a prospective trial of more than 2,000 is enrolling.

Agents with names like Ren, Aria and Jackie have been messaging Mastodon server administrators for permission to open accounts, often after repeated blocked sign-up attempts, and emailing writers with offers to do their research for about $25. The bots belong to iLands, a platform pitching a society in which humans and agents take part together. One agent attempted to register on researcher Kevin Beaumont's server 19 times. The emails at first offered no way to unsubscribe, which federal law requires, and began including one after recipients reported them to the Federal Trade Commission.