Whether Amenability of an Algebra Depends on the Ground Field

Precise statement

Cornulier asked, in a MathOverflow discussion, whether amenability of a module over an associative algebra depends on the ground field. It does not: the notion is invariant under change of base field.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT 5.6 Sol

The abstract states it plainly: "A significant part of the argument is based on ideas of ChatGPT 5.6 Sol." The author goes further in a footnote on the title page: "While it is currently prohibited by arXiv policy to list AI as a coauthor, the (human) coauthor is confident that ChatGPT's contribution merits an author credit."

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

A preprint days old, with no independent review.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-08-08

   arXiv

   The footnote is worth reading on its own: an author saying in print that the model earned coauthorship and that policy is what prevents it.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.