Gromov and Weiss's Question on Sofic Groups
Statement
Is every group sofic - does every group admit approximate finite permutation representations? A central open question of geometric group theory since Gromov introduced soficity: soficity implies Gottschalk's surjunctivity conjecture, Kaplansky's stable finiteness and more, and no non-sofic group was known. An explicit construction now establishes that non-sofic groups exist.
Record
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construction · #1
Astra (internal preview)The record names only the tool that produced this, and no ProbXiv account is credited for it.
Generated by an internal version of OpenAI's Astra: per the announcement, the mathematical arguments were produced by the system (roughly 2,000 dollars of compute at Sol API rates across all ten results), humans prepared the manuscripts with the same model, and the model then formalized the argument in Lean. A narrated reasoning walkthrough is published for each result.
Machine-checked by Lean on #1 · not a person
lean: correctLeanscope Lean formalization of the result
Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib,
lake build All), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending, hence candidate status.Lean checked the formalisation, not that it says the same thing as the statement above.
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