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arXiv · 2608.30336

An Improvement to the Upper Bound for Marton's Covering Conjecture

Zhao Song·Song Yue
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Abstract

Marton's covering conjecture studies finite sets in high-dimensional binary spaces whose pairwise sums create relatively few new elements. It predicts that every such set can be described efficiently by shifted copies of one linear subspace of comparable size. Gowers, Green, Manners, and Tao [GGMT25] proved the conjecture with exponent $12$. Liao [L24] improved the exponent to $9$. We improve it further to $5.287$.

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Zhao Song, Song Yue. 2026-09-15. An Improvement to the Upper Bound for Marton's Covering Conjecture. https://arxiv.org/abs/2608.30336

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