Facial Distance Patterns in Planar Graphs
Statement
For a designated face of an undirected unweighted planar graph, how many distinct distance patterns can vertices have? Li and Parter (STOC 2019) proved an upper bound; Mozes, Wallheimer and Weimann conjectured the true answer matches their lower bound. Proved, closing the gap.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
GPT-5.6 Sol, with Viktor Fredslund-Hansen, Shay Mozes and Oren WeimannThe 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 simple proof was found by OpenAI's GPT 5.6-Sol model", and the paper says it came from a single prompt describing the state of the art and asking for any improvement on the upper bound. The authors are candid about what that means: "It is surprising (not to say embarrasing) that this open problem has such a simple proof, which has eluded the community despite the human efforts invested in it." Section 2 of the paper is titled The ChatGPT Proof.
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