On the existence of non-sofic groups

[This is a guest post by Andreas Thom. This blog post was initially written in a different file format and converted using AI. — T.] When I woke up on August 1st, 2026, I had received a few emails from colleagues asking for my opinion on a remarkable result that had circulated the previous day. The result was a solution to a long-standing open problem in geometric group theory, specifically the existence of a non-sofic group. I was astonished and at the same time, looking at the first draft, also in a way happy to see that Kun’s work on expander decompositions and my joint work with Gábor Kun played a decisive role in the crucial Proposition 2.3 of the OpenAI paper. I had always hoped that the theory of centralizer rigidity would eventually have significant applications, but I had not found the right setting in which it could be used so effectively. In that sense, the solution also came as a relief and I was happy to explain the ideas in a post on MathOverflow a few days later. From…