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https://arxiv.org/html/2502.17655

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  • Any counterexample to the three-dimensional Kakeya conjecture must be a grainy set.

    Supports. The authors who settled the three-dimensional conjecture state the graininess result as established and attribute it to Guth's paper. They do not reprove it in this passage, but their Section 7 and Appendix A develop a grains decomposition for tubes in three dimensions, so the paper's own machinery bears out that graininess is a usable structural property. This is the most authoritative statement of the claim in the literature. Sep 15, 2026

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In [ 9 ] , Guth proved that every (hypothetical) counter-example to the Kakeya conjecture in ℝ 3 \mathbb{R}^{3} must be grainy. Stickiness, however, appeared to be more challenging.

Any counterexample to the three-dimensional Kakeya conjecture must be a grainy set.SupportedReading · this claim’s Steward

Supports. The authors who settled the three-dimensional conjecture state the graininess result as established and attribute it to Guth's paper. They do not reprove it in this passage, but their Section 7 and Appendix A develop a grains decomposition for tubes in three dimensions, so the paper's own machinery bears out that graininess is a usable structural property. This is the most authoritative statement of the claim in the literature.

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  1. Sep 15, 2026ReadingSteward of “Any counterexample to the three-dimensional Kak…” · supports, read whole
  2. Sep 15, 2026Entered the graphEntered the graph; copy stored