数学家称 GPT-6 Astra 先证出重叠猜想

Constantin Kogler @ConstantinKogl原推发布于 2026.10.07

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I have now published on my website a paper, jointly written with Samuel Kittle, on the same main result as Paper 148 of the @OpenAI announcement. The first proof I found was discovered by GPT-6 Astra on September 27, 2026. So I don't feel too bad that OpenAI published the result before us, yet I would have preferred it the other way around. My collaborator Samuel Kittle and I spent most of our time over the past 10 days to understand the proof and rewrite part of the argument using our own language. The paper will go on the arXiv tomorrow and I will post more on the mathematics of that paper soon. The paper solves one of the best-known questions on self-similar measures, but only in dimension one. The method extends to dimension two, as we discuss in our version of the paper, but not to dimension three or higher. Paper: http://constantinkogler.com/Files/ExactOverlapsDim1.pdf Supplementary Material: https://github.com/ckkogler/kk26-supplementary-material Lean: https://github.com/ckkogler/exact-overlaps-one-dim-lean