Technical Corrections and Missing Justifications in a Streamlined Proof of the Three-Dimensional Kakeya Set Conjecture

Abstract

This technical note examines version 1 of Guth, Wang and Zahl, A streamlined proof of the Kakeya set conjecture in R^3 (arXiv:2601.14411v1). It records parameter and bookkeeping defects in Theorem 7.3(B), supplies a self-contained proof of the omitted shaded slab estimate in Lemma 6.9, identifies a dimension-scope mismatch in Lemma 7.5, gives a numerical counterexample to the local/global parallel-body equality used in the proof of Lemma 7.4, and isolates the remaining Frostman-to-Convex-Wolff hypothesis-transfer question. The note does not claim that the three-dimensional Kakeya theorem or the longer Wang-Zahl proof is invalid. This public revision preserves verbatim the twelve-page manuscript completed and privately sent to Guth, Wang, and Zahl on August 16, 2026, and adds a dated notice discussing the separate August 19 preprint of Hua and Yang (arXiv:2608.18870v1) and the limited overlap between the two correction papers.