Preprint in the OpenAI Math release
A nine-dimensional counterexample to Borsuk's covering assertion
OpenAI
Abstract
The compact set of rank-one orthogonal projectors on ℝ, with the Frobenius metric, cannot be covered by ten sets of strictly smaller diameter. It therefore gives a counterexample to Borsuk's conjecture in dimension nine.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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