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Fig. 4.

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Top and middle panels: Temporal variations of the m = 1 mode amplitude extracted from Blos and Vlos data, respectively. The red, orange, green, and blue curves correspond to results from the HMI B avg + $ \langle B_{\mathrm{avg}}^{+} \rangle $, HMI V zonal $ \langle V_{\mathrm{zonal}}^{-} \rangle $, GONG B avg + $ \langle B_{\mathrm{avg}}^{+} \rangle $, and GONG V zonal $ \langle V_{\mathrm{zonal}}^{-} \rangle $ datasets, respectively. Shaded regions indicate the 68% confidence interval, estimated using 10 000 Monte Carlo simulations. Open circles denote instances where the excess power near the mode frequency falls below the 90% confidence level. We note that V zonal $ \langle V_{\mathrm{zonal}}^{-} \rangle $ was derived directly from the LOS Doppler velocity (Eqs. (4)–(6)); unlike LG25, we did not apply a multiplicative factor to scale the V zonal $ \langle V_{\mathrm{zonal}}^{-} \rangle $ amplitudes to match the horizontal velocities from the ring-diagram maps. Vertical lines denote key phases of the solar cycle, with solid lines representing solar minima and dashed lines indicating solar maxima. Bottom panel: Average sunspot number (source: WDC-SILSO, Royal Observatory of Belgium, Brussels, https://doi.org/10.24414/qnza-ac80).

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