What was already known
Problem 21.150 asked whether this rank inequality always holds under the stated extension and centralizer assumptions.
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
An explicit finite counterexample refutes the proposed inequality.
Limitations
The example uses p=3; it disproves the universal bound without classifying the other cases.
Technical verification
The companion metadata names declaration kourovka_21_150 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_21_150.
- Checker
- Lean 4
- Scope
- A 3-group extension G=A⋊B with elementary abelian A and B and trivial C_B(a) can have rank(Z(H)∩H′)>rank(B), where H=⟨a,B⟩.
- 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.
Read this published revision