On the existence of non-sofic groups

Andreas Thom (TU Dresden) explains that OpenAI's non-sofic group proof (1 Aug 2026, "Ten advances") relies crucially on his 2019 work with Gábor Kun on centralizer rigidity and expander decompositions (Proposition 2.3 of OpenAI's PDF). He says this contradicts OpenAI's public talk of a "decade without progress". He had discussed exactly these techniques in detail with ChatGPT and asked OpenAI whether that reached the model. Mark Sellke replied "that did not happen". Thom says the reply blurred two separate questions: whether the conversations entered training data, and whether they were available to the reasoning process. Kun and Thom posted a follow-up, arXiv 2608.06222.

• "you cannot speak in the public announcement of a decade without progress and then use a 2019 paper in a crucial way."
• "If nonpublic research supplied by users improved a model and the provider then used that model to race those users to publication—without informed consent, disclosure, or credit—that would be ethically indefensible."