Kurkov's Fubini-Number Sum Conjecture

Precise statement

For the Fubini numbers $a(n)$, is $a(n) = \sum_{k=0}^{2^{n-1}-1} A284005(k)$ for every $n > 0$, as conjectured on the OEIS in 2018?

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

Demonstrandum multi-agent pipeline

Found by the Demonstrandum multi-agent pipeline; every refutation ships a finite certificate, a mutation-tested checker, and an independent clean-room recomputation.

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

Verification boundary

unreviewed

Refined ordered-set-partition proof, audited, with an exhaustive checker; not externally refereed.

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

Timeline

1. 2026-07-08

   Demonstrandum artifacts repository (RESULTS.md)

   VibeMathed reports this item as resolved. 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.

• 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.