What was already known
The existence of a surjective, non-injective operator of this kind on a non-abelian group was an open question of Bardakov and Gubarev.
AI involvement
Van Doorn, Judin, Monticone and Morrison report that Aristotle developed the proof strategy and Lean proof without human guidance on mathematical steps. The authors chose problems, supplied infrastructure, refined the formal code, translated the proofs into prose and arranged external review.
The authors say Aristotle developed the new mathematical argument and formal proof strategy without human guidance on the mathematical steps. Humans selected the task, supplied infrastructure, refined the code and wrote the prose account.
Importance
The construction resolves that specific existence question.
Limitations
It is an existence example, not a classification of Rota–Baxter operators on groups.
Technical verification
The companion metadata names declaration kourovka_20_125 and reports a complete Lean proof with zero sorry. This is a source-reported machine check of the scoped theorem; the assessment did not compile the project.
Formal checking
The authors report a Lean 4 proof with zero sorry for declaration kourovka_20_125.
- Checker
- Lean 4
- Scope
- A non-abelian group admits a weight-one Rota–Baxter operator that is surjective but not injective, answering Problem 20.125.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Van Doorn, Judin, Monticone and Morrison translated the formal solution, refined the explanation and present the construction or proof in mathematical prose. This documents human explanation of the central argument.
Correction and publication history
Primary-source review of the scoped Kourovka result, AI contribution, Lean checking, human prose proof and prior baseline. Historical, non-notifying addition.
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