Cool application with the lynx-hare data—always fun to see historical datasets brought back to life.

Quick question on the binarization: I see you used species-specific medians (Figure 6 caption). Given that ψ and the directional kernel might be pretty sensitive to where you draw that "high/low" line, did you try other cutoffs? Maybe 33rd/67th percentiles, or mean-based?

Figure 7 shows nice recovery for the median, but I'm particularly curious whether the directional asymmetry (p3 >> p7) holds up under other thresholds—especially given that 1918 reset mentioned in the held-out analysis. That year seems like it could be a stress test for any fixed threshold.

Would be curious to hear how robust the results are. Thanks!