Rigidity spectra and onset geometry of the two largest Forbush decreases of solar cycle 25 from visibility-graph curvature

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 $\mathrm{\mid }z\mathrm{\mid }=4.7$-$23.7$. 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 $\delta$ 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 $\gamma =0.80$ (Gannon) and $0.50$ (June 2025) with $A_{10}=11.2\mathrm{\%}$ and $18.8\mathrm{\%}$: the deeper event is also spectrally harder. Across the 12 station-event pairs the curvature extreme scales with FD amplitude as $\mathrm{\mid }{\mathcal{F}}_{\min }\mathrm{\mid }\propto A^{0.57}$ (Spearman $\rho =0.75$). These results establish local graph curvature as a compact, rigidity-resolved descriptor of FD morphology.