Erdős Problem #489

Precise statement

If $A$ is a forbidden-divisor set with $|A \cap [1,x]| = o(\sqrt{x})$ and $B = \{b_1 < b_2 < \cdots\}$ the sifted set, must $x^{-1} \sum_{b_i < x} (b_{i+1} - b_i)^2$ converge to a finite limit?

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-5.6 starships (Claude Fable 5 reviewer)

Produced by the GPT-5.6 starships pipeline with Claude Fable 5 as reviewer.

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

Verification boundary

lean verified statement audited

Lean-checked; the erdosproblems.com community status is still pending, so this is a candidate rather than an accepted resolution.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-07-13

   erdosproblems.com/489

   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.