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The variant of the Kakeya problem phrased in terms of Wolff's axioms for convex sets: whether convex Kakeya/Besicovitch sets (or their associated set of directions) satisfy Wolff-type dimension axioms. Claims about the truth or failure of the convex Wolff axioms in specific dimensions, and related convexity-based constructions, belong here; the standard (non-convex) Kakeya set conjecture does not.

Every set of delta-tubes pointing in delta-separated directions satisfies the polynomial Wolff axioms in every dimension.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Harmonic analysis Kakeya conjecture Polynomial Wolff axiomsimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The convex Wolff axioms version of the Kakeya conjecture fails in dimensions four and above.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Kakeya conjecture Harmonic analysisimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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