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As an application to a model describing graphs with partial information, I found what might be an (as yet unverified) proof that $R(5,5)\leq 47$.

According to the Dynamic Survey of Ramsey Numbers at https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS1 that bound is not yet proved. However, I don't know if that survey is up to date.

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    $\begingroup$ The current best known upper bound is $48$. See here. $\endgroup$
    – Gabe Conant
    Commented Sep 18, 2019 at 16:12
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    $\begingroup$ The dynamic survey is up to date. An improvement as you indicate would certainly grant an update there. $\endgroup$
    – Andrés E. Caicedo
    Commented Sep 18, 2019 at 16:32
  • $\begingroup$ Well, upon checking, I just found an error, but I think the proof is recoverable, with a little more work and time. $\endgroup$
    – Edwin Karat
    Commented Sep 18, 2019 at 18:58
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    $\begingroup$ @Edwin, normally I don't suggest advertising proofs or proof attempts on MathOverflow. (Your reference request for an update seems fine to me.) In this case, if you have a write-up which indicates the error first and your idea for a fix, followed by a good write up, you might crowd source a solution by providing a link to the write up, either as a comment here or on your user page. Gerhard "In Case The Aliens Arrive" Paseman, 2019.09.18. $\endgroup$
    – Gerhard Paseman
    Commented Sep 18, 2019 at 23:28

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