关于具有大 systolic（最短闭测地线长度）的曲面的注记
A note on surfaces with large systoles
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中文总结 AI 辅助
该注记通过延续前期有限覆盖直径研究，采用常扭转裤形分解框架，证明亏格足够大时存在闭双曲曲面，其systole下界改进为log g级，突破此前2/9的界，证明由GPT-5.6 Sol完成。
中文摘要 AI 辅助
我们证明，对每个足够大的亏格g，存在闭双曲曲面S_g，其systole（最短闭测地线长度）sys(S_g)≥log g−12log log g。特别地，liminf_{g→∞} [max{sys(S):S∈M_g} / log g] ≥1，改进了此前已知的2/9的界。本注记是我们关于有限覆盖直径的前期工作（arXiv:2608.12887）的延续，采用相同的常扭转裤形分解框架研究systoles，证明由GPT-5.6 Sol通过与作者的深入讨论完成。
英文摘要
We show that for every sufficiently large genus $g$, there exists a closed hyperbolic surface $S_g$ with systole $\mathrm{sys}(S_g)\geq \log g-12\log\log g$. In particular, $$\liminf_{g\to \infty}\frac{\max\{\mathrm{sys}(S):S\in \mathcal{M}_g\}}{\log g}\geq 1,$$ improving the previously known bound $2/9$. This note is a continuation of our previous work on the diameter of finite covers arXiv:2608.12887, using the same framework of constant-twist pants decomposition to study systoles. The proof was developed by GPT-5.6 Sol through an extended discussion with the author.
