Erdős Problem #267

Precise statement

If $n_1<n_2<\cdots$ with $n_{k+1}/n_k\ge c>1$, must $\sum_k 1/F_{n_k}$ be irrational? The proposed proof closes the range $1<c<2$ left open by earlier criteria.

This statement is indexed from an attributed source. 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, according to the source.

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

Verification boundary

lean verified statement audited

The source reports a Lean check while the Erdős Problems community status remains pending; status therefore remains candidate.

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

Timeline

1. 2026-07-13

   erdosproblems.com/267

   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.