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 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 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 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% and 18.8%: the deeper event is also spectrally harder. Across the 12 station-event pairs the curvature extreme scales with FD amplitude as F proportional to A 0.57 (Spearman rho = 0.75). These results establish local graph curvature as a compact, rigidity-resolved descriptor of FD morphology.