Problem detail · source-aware
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The classical Abbott-Hanson recurrence gives $S(k+2) \ge 9S(k)+4$ for Schur numbers, and had stood as the basis for the best asymptotic lower bounds. Shifted $S$-templates, a more flexible form of Rowley's template construction, yield $S(k+2) \ge 10S(k)+2$ and hence improved lower bounds.
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The abstract says the shifted $S$-template construction was discovered during a conversation with ChatGPT 5.5 Pro and then refined, verified and extended to multiple templates by the authors, and the conclusion describes the paper as building on an original idea of the model.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
improves the classical recurrence; the exact Schur numbers beyond S(5) remain unknown
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.