ProofCouncil (GPT-5.5 Pro)
The upper-bound construction was found by the ProofCouncil harness running GPT-5.5 Pro.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Erdős Problem #539
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
For $|A| = n$, how small can the cofactor set $Q(A) = \{a / \gcd(a,b) : a, b \in A\}$ be? The answer is $h(n) = n^{1/2 + o(1)}$: a new upper bound $h(n) \le n^{1/2} \exp(O(\sqrt{\log n}))$ matches the classical lower bound.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
Lean record alongside the official Erdős problems update marking the exponent determined.
Correctness: supported · statement fidelity: audited · peer review: none
Timeline
-
erdosproblems.com/539
main exponent determined; sharper subpolynomial factors remain open
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.