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The three-dimensional Kakeya maximal conjecture

Full dimension of Kakeya sets and the quantitative maximal-operator estimate are different assertions.

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Understanding the problem

Read the background

Full dimension of Kakeya sets and the quantitative maximal-operator estimate are different assertions. The maximal estimate must control all permitted functions and tube placements.

This entry concerns the three-dimensional maximal estimate. The family’s four-dimensional Hausdorff result is a separate statement, and no dimension-free maximal theorem is claimed.

Why it matters

If correct, resolves the quantitative three-dimensional maximal target rather than only a set-dimension statement.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • This entry concerns the three-dimensional maximal estimate. The family’s four-dimensional Hausdorff result is a separate statement, and no dimension-free maximal theorem is claimed.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

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

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