Problem detail · source-aware
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Seymour conjectured that every oriented graph has a vertex $x$ with $|N^{++}(x)| \ge |N^{+}(x)|$. It holds for oriented graphs of minimum out-degree exactly $7$, the first improvement to the out-degree threshold since Kaneko and Locke settled degree $6$ in 2001.
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.
The CP-SAT models behind the computational part were developed with assistance from ChatGPT 5.5 Pro; the resulting OR-Tools encodings were then run and independently checked by the authors.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
The proof leans on a CP-SAT computation whose encodings the authors state they verified independently. arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
minimum out-degree 7; the conjecture is open in general
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.