基于可视性图曲率的太阳活动周期25中两次最大福布什下降事件的刚性谱与起始几何结构
Rigidity spectra and onset geometry of the two largest Forbush decreases of solar cycle 25 from visibility-graph curvature
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中文总结 AI 辅助
该研究将自然可视性图的节点福尔曼 - 里奇曲率应用于太阳活动周期25的两次最大福布什下降事件，发现其在事件起始时呈现最小值，通过测试确认该特征，还表明其对多种因素具鲁棒性，能编码更多结构，可作为FD形态的描述符。
中文摘要 AI 辅助
我们将一种几何网络诊断方法——自然可视性图（NVG）的节点福尔曼 - 里奇（FR）曲率，应用于太阳活动周期25的两次最大福布什下降（FD）事件：2024年5月10 - 11日的甘农风暴和2025年6月1日的事件。利用来自六个NM64站点的30分钟NMDB记录，跨越截止刚度$R_c \simeq 0$ - $7\,$GV，我们发现节点FR曲率在两次事件的FD起始时都呈现出尖锐、连贯的最小值，起始到平静的中值曲率比为2.5 - 5.2（甘农）和3.3 - 8.2（2025年6月）。通过保留完整自相关结构的放置（块置换）测试，确认了所有24个台站 - 相位组合在$p \lesssim 2 \times 10^{-3}$（测试下限）时的起始特征，$|z| = 4.7$ - $23.7$。该特征对福尔曼曲率的边加权和滑动窗口（6 - 24小时）图构建具有鲁棒性，并且幅度盲（水平可视性）控制证实它特定于下降的幅度几何结构。节点FR曲率使仅从NVG度序列获得的效应大小几乎翻倍（平均克利夫δ为0.89对0.54），因为它编码了两跳（邻居度）结构。通过多曼耦合函数折叠台站幅度得到FD光谱指数$\gamma = 0.80$（甘农）和$0.50$（2025年6月），$A_{10} = 11.2\%$和$18.8\%$：更深的事件在光谱上也更硬。在12个台站 - 事件对中，曲率极值与FD幅度成比例缩放，$|\mathcal{F}_{\min}| \propto A^{0.57}$（斯皮尔曼$\rho = 0.75$）。这些结果确立了局部图曲率作为FD形态的紧凑、刚度分辨描述符。
英文摘要
We apply a geometric network diagnostic -- the nodal Forman-Ricci (FR) curvature of natural visibility graphs (NVG) -- to the two largest Forbush decreases (FDs) of solar cycle 25: the Gannon storm of 2024 May 10-11 and the 2025 June 1 event. Using 30-min NMDB records from six NM64 stations spanning cutoff rigidities $R_c \simeq 0$-$7\,$GV, we show that nodal FR curvature exhibits a sharp, coherent minimum at FD onset in both events, with onset-to-quiet median curvature ratios of 2.5-5.2 (Gannon) and 3.3-8.2 (June 2025). A placement (block-permutation) test that preserves the full autocorrelation structure confirms the onset signature at $p \lesssim 2 \times 10^{-3}$ (the floor of the test) for all 24 station-phase combinations, with $|z| = 4.7$-$23.7$. The signature is robust to edge weighting of the Forman curvature and to sliding-window (6-24 h) graph construction, and an amplitude-blind (horizontal-visibility) control confirms that it is specific to the amplitude geometry of the decrease. Nodal FR curvature nearly doubles the effect size obtained from the NVG degree sequence alone (mean Cliff's $δ$ of 0.89 vs 0.54), because it encodes two-hop (neighbor-degree) structure. Folding the station amplitudes through the Dorman coupling function yields FD spectral indices $γ= 0.80$ (Gannon) and $0.50$ (June 2025) with $A_{10} = 11.2\%$ and $18.8\%$: the deeper event is also spectrally harder. Across the 12 station-event pairs the curvature extreme scales with FD amplitude as $|\mathcal{F}_{\min}| \propto A^{0.57}$ (Spearman $ρ= 0.75$). These results establish local graph curvature as a compact, rigidity-resolved descriptor of FD morphology.
