GPT-5.6 Sol Generates a Borsuk Counterexample in Dimension 63

In a preprint first uploaded on August 12, 2026, Yibo Ji presents a 321-point subset of $\mathbb{R}^{63}$ that cannot be partitioned into 64 sets of smaller diameter. The construction therefore gives $b(63)\geq65$ and supplies a counterexample to Borsuk's proposed $d+1$-part partition bound in dimension 63.

The construction begins with the Euclidean representation of the $G_2(4)$ strongly regular graph and the Jenrich-Brouwer 320-point core in a 63-dimensional subspace. It adds one projected and rescaled point while preserving the graph-clique obstruction: every smaller-diameter subset contains at most five points, so 64 such subsets cannot cover all 321 points. The paper includes a Python verification program that reconstructs the relevant graph data and checks the clique bound.

The preprint states that ChatGPT using GPT-5.6 Sol generated the example and proof in their entirety. Ji reports personally verifying the result and accepting responsibility for that verification, while explicitly declining credit for the construction's originality. The claim remains an unverified preprint result.