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Erdős Problem #1091

Combinatorics · posed by Paul Erdős, 1976 · solved

2 comments

Statement

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

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

  1. proof attempt · #1

    OpenAI internal model, with Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke and Gregory Valiant

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

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

    From "Short proofs in combinatorics, probability and number theory II": "The proofs in this manuscript are due to an internal model at OpenAI... The role of the human authors was simply to digest the proofs and modify the write-ups for clarity and elegance." This is the one place in the paper where the humans changed the mathematics: the model's original proof gave the same family of example graphs but deduced colour-criticality from a presentation the authors reworked.

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed site check

    scope Reproduction by the VibeMathed site

    Marked solved by erdosproblems.com's official status. Solve credited via Terence Tao's AI-contributions wiki.

    Repeated from the source; nothing was checked here.

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