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    $\begingroup$ Yes, Sam, this was the answer I planned to post! $\endgroup$ Commented Mar 26, 2021 at 14:53
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    $\begingroup$ Andrew Suk proved an asymptotic statement gilkalai.wordpress.com/2016/05/04/… $\endgroup$ Commented Apr 27, 2022 at 19:01
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    $\begingroup$ I took a poll among experts in a recent conference about "discrete convexity and geometry" and there were more than twice who believe the conjecture is true compared to those who believe it is false. $\endgroup$ Commented Oct 5, 2023 at 6:43
  • $\begingroup$ This would be a fascinating example of the Law of small numbers, If correct. $\endgroup$ Commented Feb 22 at 18:21