Problem detail · source-aware
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Han and Xiong extended the Gaussian binomial coefficient to positive rational index and conjectured that its integer trace, the integer-exponent part of the resulting power series, is coefficientwise largest at the integer point. Ono's paper proves a support-dominance theorem settling the conjecture for a large family of rational parameters and reduces the full conjecture to unit fractions, with a finite computer verification covering every remaining case up to a fixed bound.
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The theoretical results were autonomously produced and verified in Lean by AxiomProver: the formal statements and proofs of Theorem 1.3, Corollary 1.4 and Theorem 1.5 were generated from a natural-language statement of the problem containing no proofs, then checked by the Lean proof assistant. An appendix records precisely what was and was not supplied to the system.
Provider: Axiom Math · Prompt public: unknown · Independence: unknown
The main theorems were formalized and kernel-checked in Lean by the same system that produced them; the human author wrote the paper from that formal development. Tier: AxiomProver generated the formal statements and proofs from a natural-language prompt; nobody independent has audited the statement fidelity.
Correctness: supported · statement fidelity: unaudited · peer review: none
Settles the conjecture for a large family and reduces the rest to unit fractions; the general unit-fraction case remains open.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.