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Borsuk’s covering question in dimension nine

Borsuk’s covering question asks whether a bounded set in d dimensions can be partitioned or covered by d+1 subsets of strictly smaller diameter.

Progress records 1

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1 record · How we rate progress

Understanding the problem

Read the background

Borsuk’s covering question asks whether a bounded set in d dimensions can be partitioned or covered by d+1 subsets of strictly smaller diameter. A counterexample is specific to a dimension and construction.

Read the claim in its exact mathematical setting. A manuscript is a research report; its presence in this catalog does not establish that the proof has been independently verified or that the historical novelty assessment is complete.

Why it matters

A focused research target whose precise scope can be followed separately from the general capability of an AI system.

What counts as progress

A sourced new theorem, construction, bound, algorithm, or formalization with its baseline and evidence stated.

What to watch for

  • Check the formal statement, assumptions, and cited prior results against the claimed improvement.
  • Keep author-reported checking, independent checking, and manuscript availability separate.
  • Track revisions to the pinned source and any subsequent expert assessment.

Background review: 2026-10-11. Selected sources:

Website timeline

Publication dates and editorial changes.