AlphaProof Nexus
Proved by AlphaProof Nexus with a Lean-checked argument.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Erdős Problem #138
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
If $W(k)$ is the least $N$ such that every two-colouring of $\{1, \dots, N\}$ contains a monochromatic $k$-term arithmetic progression, must $W(k+1) - W(k) \to \infty$?
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; official Erdős problems record updated.
Correctness: supported · statement fidelity: audited · peer review: none
Timeline
-
erdosproblems.com/138
the stronger question $W(k)^{1/k} \to \infty$ 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.