An AI Generated Counterexample to Borsuk Problem in Dimension 63

Abstract

We construct a 321 point set in R^63 that cannot be partitioned into 64 subsets of smaller diameter, proving b(63)>=65. Starting from the G_2(4) Euclidean representation and the Jenrich Brouwer 320 point core in dimension 63, we add one projected and rescaled point while preserving the relevant clique obstruction. The example and proof were generated entirely by ChatGPT using GPT 5.6 Sol. The author has personally verified the result and assumes responsibility for that verification, but claims no credit for the originality of the construction.

Just found out that this counterexample had already been posted elsewhere: https://github.com/maaxgrin/borsuk-63-counterexample and https://nickk124.github.io/borsuk/