Examining Kakeya's n=4 Under Dynamic Euclidean Geometry

摘要 / Abstract 中文摘要 本文在动态欧氏几何(Dynamic Euclidean Geometry, 见 zhang 2026a)框架下审视 Kakeya 问题在 ℝ⁴ 中的 Hausdorff 维数。核心观察:在四维空间中,三维本身自带的多维度手性在法向移动中自然会带来空间的不均匀性;特殊的四维需要特殊的三维法向移动实现。因此合法 Kakeya 集在 ℝ⁴ 中 Hausdorff 维数 = 4,但覆盖非光滑均匀填充,而是带有结构性手性褶皱。本文将此视为操作几何框架下的探讨性注记,不声称提供解析证明,供学界检验。 English Abstract This paper examines the Hausdorff dimension of the Kakeya set in ℝ⁴ under the framework of Dynamic Euclidean Geometry (see zhang 2026a). Core observation: in four-dimensional space, the multi-dimensional chirality inherent to 3D naturally introduces spatial inhomogeneity during normal translation; special 4D requires special 3D normal translation. Thus the Hausdorff dimension of a legitimate Kakeya set in ℝ⁴ equals 4, but the covering is not a smooth uniform fill—it carries structural chiral folding. This is presented as an exploratory note under the operational-geometric framework; no analytical proof is claimed. The author welcomes examination by the academic community.