What was already known
Earlier work implied abstract existence of non-MF C*-algebras. Kun and Thom’s non-sofic examples, built from earlier OpenAI examples, supplied Eckhardt’s starting point.
AI involvement
Eckhardt says ChatGPT 5.6 Sol generated the examples and proof ideas after he chose the Kun–Thom direction. He internalized and rewrote the arguments; Willett and Fournier-Facio contributed separate observations and an extension.
The paper directly credits the model with the examples and proof ideas; Eckhardt chose the starting point and later refined the paper, while the named human extensions retain separate credit.
Importance
The explicit group construction gives a concrete operator-algebraic example beyond abstract existence.
Limitations
Scott Sauer reports similar independent AI-assisted work, leaving priority unclear. No completed check of Eckhardt’s proof is documented; Rufus Willett identified the related non-finite full-algebra consequence separately.
Technical verification
A complete paper argument is available, and the author says he internalized it, but the source documents no completed check of the assessed proofs. Helpful comments and Sauer's separate planned Lean proof do not verify Eckhardt's theorems.
Human understanding
Eckhardt expressly says he internalized the ideas and wrote the exposition to make the main mechanism visible to mathematicians; Sections 3–4 explain the Kazhdan-projection and cocycle steps.
Correction and publication history
The explicit group construction gives a concrete operator-algebraic example beyond abstract existence.
Read this published revision