An AI Generated Counterexample to Borsuk Problem in Dimension 63
Yibo Ji
Abstract
We construct a 321 point set in R63 that cannot be partitioned into 64 subsets of smaller diameter, proving b(63)>=65. Starting from the G2(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.
Create a lesson
Related papers
Uncentered Blaschke-Santaló inequalities for the Gaussian measure
S. Artstein-Avidan, M. Fradelizi, K. Wyczesany
Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions
Martin Lotz
CAT(0) square complexes that do not embed into finite products of trees
James Davies, Harry Petyt
On Strong Bi-Lipschitz Triviality of Deformations
Debomita Chakraborty, Saurabh Trivedi
Greedy Packing of Nested Rings: Placement Rules, a Golden Counterexample, and a Tribonacci Floor
Javier Aguilar Martín
Strong laws, random monotone vector fields and gradient flows on metric spaces of nonpositive curvature
Nicholas Pischke