What was already known
Han and Xiong proved k≤3 and certain integer and half-integer families, and checked r=1/3 and 1/4 through k=150. The full comparison was open.
AI involvement
Ken Ono reports that AxiomProver received the target statements and Han–Xiong paper without proofs, then generated the three theoretical statements and Lean proofs. Ono wrote the human explanation.
The three selected theoretical results and proofs were produced by AxiomProver from stated targets without supplied proofs; later human exposition does not change their origin.
Importance
Proves the conjectured comparison on the full half-line r≥1/2 and narrows the remaining problem to a canonical family.
Limitations
The all-parameter, all-k conjecture remains open. A separate exact computation reaches k≤200; it is outside the three reported Lean proofs. Ono checked the formal statement correspondence, not every proof step by hand.
Technical verification
The paper reports sorry-free Lean 4.31 proofs for exactly Theorem 1.3, Corollary 1.4 and Theorem 1.5, and a human check that the formal statements express those results. The separate finite k <= 200 theorem is outside this formalized scope.
Formal checking
Sorry-free formal proof of the three statements; Ono checked their correspondence to the paper; source-reported.
- Checker
- Lean proof assistant, with statement alignment checked by Ken Ono
- Scope
- Support dominance, its r >= 1/2 corollary and canonical reduction, as Theorem 1.3, Corollary 1.4 and Theorem 1.5
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Ono's Sections 1–3 explain the central support nesting and exponent-shift argument behind the three theoretical results.
Correction and publication history
Proves the conjectured comparison on the full half-line r≥1/2 and narrows the remaining problem to a canonical family.
Read this published revision