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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

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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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Ting-Wei Chao, Zixuan Xu and Dmitrii Zakharov, using ChatGPT 5.4 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    "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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Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.