Erdős Problem #522

Precise statement

For $P_n(z) = \sum_{k=0}^n \varepsilon_k z^k$ with independent uniform signs, does the number $R_n$ of roots in $|z| \le 1$ satisfy $R_n/(n/2) \to 1$ almost surely? The manuscript proves the strong law with $R_n = n/2 + O_\omega(n^{149/150})$.

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

GPT-5.5 Pro

The source does not provide a sufficiently specific role description.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Public manuscript; a full expert review has not been located.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-04-20

   erdosproblems.com/522

   VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

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.

• The source status is candidate and must not be represented as solved.
• 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.