GPT-5
The acknowledgements state the key construction idea was suggested during an interaction with GPT-5.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Improved Bound for Colorings Without Symmetrically Colored k-APs
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Deng, Tidor and Zhao asked whether $[N]$ admits a coloring with $N^{o(1)}$ colors and no symmetrically coloured 4-term arithmetic progression, giving an $O(N^{\log_{22}3})$ coloring. The paper gives an $O_k(N^{4/k^2})$ coloring of $[N]$ avoiding symmetrically coloured $k$-APs for every even $k\ge4$, improving the exponent.
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
No independent review. The model is credited with the key construction idea rather than the surrounding analysis. Preprint, not refereed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
-
arXiv
Improves the exponent rather than answering the asked question: whether an $N^{o(1)}$ colouring exists remains open.
Known method families
construction (source-reported)
Source-reported tools: construction.
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.