Work

A local concentration correction in Hua and Yang's cellular Kakeya reduction

Year: 2026

Type: preprint

Abstract: This technical note concerns equation (9.5c0), page 40, of Hua and Yang's Cellular Maximal-Density Factoring and a Conditional Repair of the Streamlined Three-Dimensional Kakeya Reduction, arXiv:2608.18870v3 (26 August 2026). A singleton fine tube inside one coarse tube gives an explicit counterexample to the displayed all-convex Frostman bound. The note states and proves a restricted-test transfer, including the denominator loss from selecting a color, and proposes retaining the weaker test-class estimate in the source-call record. It does not claim that Proposition 9.7, the main cellular results, the conditional Kakeya application, or the three-dimensional Kakeya theorem is false. No novelty claim is made for the elementary transfer estimate. The manuscript discloses AI assistance and has not been independently refereed.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22122678

Author: Zeraoulia, Rafik

Institutions: Université Djilali Bounaama Khemis Miliana, Amar Telidji University of Laghouat

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204446699

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