arXiv:2610.21975v1 Announce Type: cross Abstract: Let $X_1,X_2,\ldots$ be i.i.d. random variables with zero mean and variance $\sigma^2\in(0,\infty)$. In this paper, we establish a sharp Cram\'er-type moderate deviation for the self-normalized maximum of partial sums under a finite $p$-th absolute moment, $2Source:https://arxiv.org/abs/2610.21975