What was already known
Cornulier asked whether algebra amenability depends on the ground field. Field independence was known for group algebras, but not arbitrary associative algebras or modules.
AI involvement
Greenfeld credits ChatGPT 5.6 Sol with the central ideas of the going-up proof. He found gaps through discussion, wrote the manuscript and proved the complementary direction; Bartholdi suggested the module extension.
The author specifically credits ChatGPT with the core mathematical ideas in §2 of the proof, while describing a joint discussion and separate human work on the final theorem.
Importance
The equivalence answers the ground-field question in the stated generality.
Limitations
The model-origin step is the core going-up argument; Greenfeld supplied the going-down proof and the final module theorem. No completed separate check of the full proof is documented.
Technical verification
The v1 manuscript gives proofs of the going-up and going-down implications, but its author-responsibility statement is not an explicit completed human proof check, and no machine check is documented.
Human understanding
Greenfeld describes the back-and-forth that exposed gaps and presents and explains the base-extension optimality and descent constructions in §§2–3. This supports understanding of the model-origin going-up mechanism.
Correction and publication history
If correct, the equivalence answers the ground-field question in the stated generality.
Read this published revision