The problem
A group is sofic if its Cayley graph can be approximated arbitrarily well by finite permutation graphs (Weiss, 2000, building on Gromov's 1999 definition). Every known family of groups is sofic. Question: does a non-sofic group exist?
Existence of Non-Sofic Groups
AI-resolvedReferences
History & significance
Soficity connects to stability of dynamical systems, the Gottschalk surjunctivity conjecture, and Connes's embedding problem. Twenty-five years of candidate obstructions (trace methods, determinant conjectures) all failed to separate any group from the finite world.
The resolution (solved by AI)
Announced by OpenAI, 1 August 2026: an internal model ("Astra") produced a construction establishing the existence of non-sofic groups — the separation twenty-five years of human effort could not find. Part of a ten-result batch spanning operator algebras, coding theory and complexity, each accompanied by Lean-formalised certificates and expert review. As with all very recent claims, the community's digestion is ongoing; the announcement marks the boldest single batch of AI-originated group theory to date.