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Uniform Witnesses for Uniform Set Systems: the k=3 Question

Combinatorics · posed by Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov (in the paper's first version), 2026 · solved

1 attempt

Statement

In the Frankl-Pach-Erdős circle of VC-dimension problems, the first arXiv version of the paper posed the k=3k=3 case of a witness construction question. ChatGPT 5.4 Pro answered it; the published construction generalizes the model's response, and the conversation transcript is public.

Context

A question posed publicly in the paper's own first version, inside the well-known Frankl-Pach VC-dimension problem circle; weeks old when answered, but documented and independently checkable.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionChatGPT 5.4 Pro with Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
    models
    ChatGPT 5.4 Pro
    people
    Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov

    "In an earlier arXiv version of this paper, Theorem 1.6 was stated as a question in the special case k=3. ChatGPT 5.4 Pro managed to successfully answer this question and the construction in Section 3.2 is a generalization of its response" - with the chat transcript linked in the paper.

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