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A Fraction Dimensional Kakeya Compression
Abstract
Recently, it was shown in arXiv:2607.27629 that under a very general condition, a generic family of curved Kakeya sets in ℝ3 not trivially contained in a hypersurface has Hausdorff dimension strictly greater than 2. In this paper we leverage large language models to give an explicit construction of a family of curves failing the worst compression phenomenon in arXiv:2607.27629, but whose union has Hausdorff dimension and upper box dimension 5/2. The example shows that there are Kakeya compression phenomena besides the trivial example of concentrating near a hypersurface. This answers a question raised in section 1.9 of arXiv:2607.27629. The models used are ChatGPT 5.6 Sol and ChatGPT 6 Astra.
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BibTeX
@misc{du2026fraction,
title = {{A Fraction Dimensional Kakeya Compression}},
author = {Jiahan Du},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05404},
eprint = {2610.05404},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05404},
}
RIS
TY - UNPB
TI - A Fraction Dimensional Kakeya Compression
AU - Jiahan Du
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05404
UR - https://arxiv.org/abs/2610.05404
AB - Recently, it was shown in arXiv:2607.27629 that under a very general condition, a generic family of curved Kakeya sets in ℝ^3 not trivially contained in a hypersurface has Hausdorff dimension strictly greater than 2. In this paper we leverage large language models to give an explicit construction of a family of curves failing the worst compression phenomenon in arXiv:2607.27629, but whose union has Hausdorff dimension and upper box dimension 5/2. The example shows that there are Kakeya compression phenomena besides the trivial example of concentrating near a hypersurface. This answers a question raised in section 1.9 of arXiv:2607.27629. The models used are ChatGPT 5.6 Sol and ChatGPT 6 Astra.
ER -