Problem detail · source-aware
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Ji, Li and Wang conjectured in 2024 that every parallel chip-firing game on a finite connected graph whose chip count lies strictly between $2|E|-|V|$ and $2|E|$ has period exactly 2, generalizing the middle rung of Levine's devil's staircase from complete graphs to all graphs. Known before only for trees, cycles, complete and complete bipartite graphs.
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 paper presents the proof plainly as found by the model: "The proof presented in Section 3 was found by the large language model GPT-5.6-Sol. The authors verified the resulting argument and take full responsibility."
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Beyond the authors' own verification, the acknowledgments thank David Ji and Michael Li, two of the conjecture's posers, for assisting with reviewing the proof.
Correctness: supported · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.