I see what you’re saying, but note that as mentioned above I did edit the post based on your feedback to be precise, stating that the conjecture we disproved wa

I see what you’re saying, but note that as mentioned above I did edit the post based on your feedback to be precise, stating that the conjecture we disproved was that regardless of the center color the chessboard of 1s could be assumed wlog in any finite diamond . (Also this is stated correctly in the paper, which at the end is the “source of truth”) I agree with you that just saying “D_r can be colored with k colors iff it can be done with a chessboard pattern of 1s” is a slightly different statement to which our counterexample is not a counterexample, but I think you got trapped into my initial omission in the blog post, which was a writing mistake rather a mathematical mistake. I don’t think there’s anything wrong here, but sorry for the original version of this post being sloppy in the writing. I agree again with what you were saying some messages ago about how versions of the conjecture that do not consider the center color can be more mathematically interesting. A proof that D_r can be colored with k colors iff it can be done with the chessboard pattern would definitely be super nice.