https://news.ycombinator.com/item?id=47497757 Solution Update: This problem has been solved! A solution was first elicited by Kevin Barreto and Liam Price, using GPT-5.4 Pro. This solution was confirmed by problem contributor Will Brian, and will be written up for publication. A full transcript of the original conversation with GPT-5.4 Pro can be found here and GPT-5.4 Pro’s write-up from the end of that transcript can be found here. Brian’s comments: “This is an exciting solution to a problem I find very interesting. I had previously wondered if the AI’s approach might be possible, but it seemed hard to work out. Now I see that it works out perfectly. It eliminates an inefficiency in our lower-bound construction and in some sense mirrors the intricacy of our upper-bound construction. The matching lower and upper bounds are quite good for Ramsey-theoretic problems, and I’m interested in further understanding why this works out so well.”