GPT-5.5 Pro, Codex 5.5
The bounds were developed with GPT-5.5 Pro and Codex 5.5.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Erdős Problem #1039
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 $f(z) = \prod_{i=1}^n (z - z_i)$ with all $|z_i| \le 1$, let $\rho(f)$ be the radius of the largest disc contained in $\{z : |f(z)| < 1\}$. Is $\rho(f) \gg 1/n$? The worst case is now known to be $\Theta(1/n)$, with the explicit bound $\rho(f) \ge (\log 2)/n$.
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-checked and expert-vouched; official record updated.
Correctness: supported · statement fidelity: audited · peer review: none
Timeline
-
erdosproblems.com/1039
order of magnitude determined; the exact asymptotic constant remains open
Known method families
argument (source-reported)
Source-reported tools: argument.
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.