The Middle Stair of Parallel Chip-Firing
Statement
Ji, Li and Wang conjectured in 2024 that every parallel chip-firing game on a finite connected graph whose chip count lies strictly between and 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.
Record
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Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
GPT-5.6 Sol, with Daniel Wang and Nathan LannanThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
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."
Recorded elsewhere on #1 · not checked here
recorded: correctVibeMathed expert verification (imported)scope Expert review reported upstream; the reviewer has no probXiv account and is not credited here
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.
Repeated from the source; nothing was checked here.
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