AI 中文总结
该研究针对p>2的所有lp范数，给出从3SAT到M^ε-GapSVP_p的确定性多项式时间归约，证明对应SVP问题的多项式因子确定性NP-难解性。
AI 中文摘要
对于每个常数2<p<∞及每个常数0<ε<min{(p-2)/(4p),1/8}，我们给出从3SAT到M^ε-GapSVP_p的确定性多项式时间归约，其中M为格的秩；对于p=∞，每个常数0<ε<1/8时同样成立。该归约基于OpenAI的多项式间隙CVP构造，以及Hair和Sahai[STOC'26]针对p>2的直接SVP归约。
英文摘要
For every constant $2<p<\infty$ and every constant \[ 0<\varepsilon< \min\left\{\frac{p-2}{4p},\frac18\right\}, \] we show that the $\ell_p$-shortest vector problem for lattices of rank $M$ is NP hard to approximate within a factor of $M^\varepsilon$, via a deterministic reduction. For $p=\infty$, the same holds for every constant $0<\varepsilon<1/8$. The reduction builds on the polynomial-gap CVP construction of OpenAI [OpenAI 2026] and the direct reduction to SVP for $p>2$ of Hair and Sahai [STOC'26].
