Uniform Witnesses for Uniform Set Systems: the k=3 Question
In the Frankl-Pach-Erdős circle of VC-dimension problems, the first arXiv version of the paper posed the 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.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Extremal set theory
- Posed by
- Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov (in the paper's first version)
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-03
- Model
- ChatGPT 5.4 Pro
- Vendor
- OpenAI
- Collaborators
- Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 8 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
"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.