What was already known
Amdeberhan, Medina and Moll conjectured nonintegrality for every n≥5. Earlier congruence work excluded integers on a set of density 120/817.
AI involvement
Ono supplied the target statements and the unformalized asymptotic estimate; AxiomProver generated the central Lean proofs. Ono wrote the mathematical exposition.
The model carried out the central formal proofs, while a human gave detailed target statements and the paper's asymptotic component.
Importance
The formalized barriers support a density-one result for the conjecture.
Limitations
The conjecture for every n≥5 remains open. Ono’s asymptotic kernel estimate and the final density-one deduction are outside the Lean proof scope.
Technical verification
For the assessed AI-generated three theorems, the paper and repository report fully sorry-free Lean 4.28.0 proofs with no new axioms. The logarithmic growth of K_n and resulting full density-one deduction are in Ono's exposition and are outside this machine-check scope.
Formal checking
Sorry-free formal proofs, reported to add no axioms
- Checker
- Lean 4.28.0 on AxiomProver's solution.lean
- Scope
- The divisibility barrier, proximity lemma and O(log N) exceptional-set bound in Appendix A
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Ono's Sections 2–3 explain the Gaussian-norm divisibility and angle-proximity counting mechanisms for these results, and distinguish the analytic lemma. The existence of a human mathematical explanation is documented.
Correction and publication history
The formalized barriers support a density-one result for the conjecture.
Read this published revision