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Erdős Problem #593

Combinatorics · candidate

2 comments

Statement

Which finite triple systems occur in every triple system of uncountable chromatic number? The claimed characterization: exactly those that, after removing isolated vertices, are linear, have every hyperedge-node of their Levi graph meeting a bridge, and have every Berge cycle even.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    ChatGPT + Aristotle

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    VibeMathed records no account of how ChatGPT + Aristotle was used here. See erdosproblems.com/593.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked end to end; not yet conventionally refereed or incorporated by the community tracker.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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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.