Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 156-01. A nine-dimensional counterexample to Borsuk's covering assertion
Manuscript map · lines 5375–5384
OpenAI@2026-10-07#rem:oai-p-156-01
Authors: OpenAI. Family 156.
Title: A nine-dimensional counterexample to Borsuk's covering assertion.
Abstract: The compact set of rank-one orthogonal projectors on ℝ4, 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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