Delay time of GCR modulation with respect to the SSN, derived using mutual information. The meaning of red and blue markers and shaded bands is the same as in Figure 7. We also include results from previous works by Shen et al. (2020), Tomassetti et al. (2022), shown as green markers and lines. To ensure consistency for comparison, the calculation window for determining delay time in panel (a) has been adjusted as follows: A < 0 covers June 1980 to September 1989, and A > 0 covers April 1991 to June 1999. The relatively small error bars in panel (a) result from the lower uncertainty of the IMP-8 data compared to the SOHO/EPHIN and AMS-02 data.