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OpenAI says its internal models proved Sogge's local smoothing conjecture in every dimension, which also settles the Kakeya and Stein restriction conjectures, and refuted the Exponential Time Hypothesis with a deterministic algorithm that counts k-SAT solutions in subexponential time. Both proofs were checked in Lean. A third result, in quantum field theory, is being held back while outside physicists write it up.
Ben Thompson reads Anthropic's prospectus as showing a very profitable core business that competition may still strip of its profits, with a structure that sets investors up for endless dilution.
Microsoft is offering voluntary exit packages to about 60,000 employees, roughly 27% of its 223,000-person workforce, in the US, Canada, India and the UK. It follows a smaller buyout plan in the spring and 4,800 job cuts in July. The company reports quarterly earnings Wednesday, with its stock near an all-time high.
A week before Election Day, the NPR/PBS News/Marist poll finds Democrats favored to win the House and Trump's approval at 38% among registered voters. Marist's first likely-voter screen of the cycle narrows things slightly, and enthusiasm is lagging among key groups. Cost of living tops voters' concerns, and a third say they faced financial hardship in the past year.
