Improve C28 upper bound to 63#84
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This PR records a construction of a counterexample to Borsuk's conjecture in dimension$63$ . Equivalently, it improves the recorded upper bound for $C_{28}$ from
to
The construction starts from the standard$G_2(4)$ Euclidean representation used in the Bondarenko and Jenrich--Brouwer constructions. The new step is to remove a structured set of $96$ points so that the remaining $320$ points lie in a $63$ -dimensional subspace, then adjoin one projected point while preserving the clique obstruction: every subset of smaller diameter has size at most $5$ .
The proof PDF, verification script, exported DIMACS certificates, and optional Sage verification of the exported certificates are available here:
https://github.com/maaxgrin/borsuk-63-counterexample
The construction and proof were obtained with assistance from GPT-5.5 Pro.