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

Precise statement

In the Frankl-Pach-Erdős circle of VC-dimension problems, the first arXiv version of the paper posed the $k=3$ 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.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT 5.4 Pro

"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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

No verification note supplied.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-03-01

   arXiv

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.