AI 中文总结
XMST提出一种结合渗流分析与Jenks自然断点的扩展最小生成树框架，通过客观断裂尺度识别恒星结构，在蒙特卡洛验证中实现高完备度与稳健性。
AI 中文摘要
我们提出了XMST，一种扩展的最小生成树框架，用于利用客观的、数据驱动的断裂尺度判据来识别空间上连贯的恒星结构。XMST将渗流分析与Jenks自然断点优化相结合，在确定最终断裂尺度之前，将MST边长分布限制在亚临界区间。该方法通过1000次受控蒙特卡洛实现进行了验证，其中包含八个经验恒星关联模板，包括一对故意重叠的模板。渗流-Jenks断裂尺度具有高度可重复性，中位数为17.028 pc，实现间标准差为0.066 pc。注入结构的平均完备度为0.9996，平均纯净度为0.7413，而备选的CDF和Mean Edge准则选择了显著更大的断裂尺度，并产生了明显较低的纯净度。将已公布的距离不确定性通过额外的10,000次XMST重建进行传播，得到的断裂尺度绝对变化中位数仅为0.282 pc。在这些扰动下，平均完备度为0.8605，平均纯净度为0.7126，而99.30%的注入模板案例继续满足所采用的检测准则。个体成员资格稳定性较低，外围和局部稀疏的成员显示出比结构核心更低的持续性。故意重叠的对在1000次实现中仅15次在空间上被分辨；基于红化的后处理诊断将其提高到446次，尽管伴随相应的完备度-纯净度权衡。因此，XMST为识别候选恒星结构及其稳定核心提供了一种稳健的方法，而详细的外围成员资格和强重叠群体则需要额外的天体物理信息。
英文摘要
We present XMST, an extended minimum spanning tree framework for identifying spatially coherent stellar structures using an objective, data-driven fracture-scale criterion. XMST combines percolation analysis with Jenks Natural Breaks optimisation, restricting the MST edge-length distribution to the subcritical regime before determining the final fracture scale. The method was validated using 1000 controlled Monte Carlo realisations containing eight empirical stellar-association templates, including a deliberately overlapping pair. The Percolation-Jenks fracture scale was highly reproducible, with a median of 17.028 pc and a between-realisation standard deviation of 0.066 pc. The injected structures were recovered with a mean completeness of 0.9996 and mean purity of 0.7413, while alternative CDF and Mean Edge criteria selected substantially larger fracture scales and produced markedly lower purities. Propagation of the published distance uncertainties through 10,000 additional XMST reconstructions produced a median absolute fracture-scale change of only 0.282 pc. Under these perturbations, mean completeness was 0.8605 and mean purity 0.7126, while 99.30 per cent of injected-template cases continued to satisfy the adopted detection criterion. Individual membership was less stable, with peripheral and locally sparse members showing lower persistence than structural cores. The deliberately overlapping pair was resolved spatially in only 15 of 1000 realisations; a reddening-based post-processing diagnostic increased this to 446, although with a corresponding completeness-purity trade-off. XMST therefore provides a robust method for identifying candidate stellar structures and their stable cores, while detailed outer membership and strongly overlapping populations require additional astrophysical information.
