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This paper aims to provide a possible derivation path for the Kakeya endpoint conjecture in dimensions n≥4.

July 27, 2026Open Access

V5-偏元数学框架下对挂谷终极大猜想(n≥4,维数部分)的初步论证——基于方向偏好场全方向覆盖投影的尝试 (V5-A Preliminary Attempt on the Kakeya Endpoint Conjecture (n≥4, Dimension Part) under the Partial-Deviation Mathematics Framework: Based on the Omnidirectional Coverage Projection of the Orientation Preference Field)

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This paper aims to provide a possible derivation path for the Kakeya endpoint conjecture in dimensions n≥4.
Utilized a framework based on Prenary Mathematics focusing on Non-Zero Subtraction and Normalization Constraint axioms.
Completed a derivation chain proving Hausdorff dimension of Kakeya sets equals n without relying on existing methods.
Formulated three independent falsifiable predictions regarding Kakeya sets and tube density.
Predicted a lower bound constant C₄≈0.786 for n=4, diverging from previously suggested values.
Identified an upper bound for tube density variation rates in non-convex regions (≤ approx. 4.67).
Observed periodic fluctuations in the convergence rate of Kakeya set dimensions with magnitude F₁≈0.0274.

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Randomized trial attempts to derive Kakeya conjecture outcome in multi-dimensional spaces, suggesting new theoretical insights.

Song Chen (2026) studied this question.

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