AI 中文总结
该研究针对马尔顿覆盖猜想，将其已证指数从9进一步提升至8.873，推动了该组合数学问题上界的改进。
AI 中文摘要
马尔顿覆盖猜想研究高维二元空间中的有限集，其两两和能产生相对较少的新元素，该猜想预测这类集合均可由大小相当的某个线性子空间的平移副本高效描述。Gowers、Green、Manners和Tao[GGMT25]证明了指数为12的该猜想，Liao[L24]将指数改进为9，我们进一步将其改进至8.873。
英文摘要
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 $5.287$.
