Normalised distribution of D_fil for all merging galaxies (dashed orange line) compared to the non-merging galaxy population (dotted blue line). Left: Distribution for galaxies across the entire cluster region (r < 5 × R₂₀₀). Middle: Galaxies in the inner cluster region (r < R₂₀₀). Right: Galaxies in the cluster outskirts (R₂₀₀ < r < 5 × R₂₀₀). For visualisation purposes, the distances to filaments have been truncated at 2 Mpc, beyond which the galaxy density drops consistently below ∼0.2. Error bars correspond to Poisson uncertainties in each bin, while vertical lines mark the median of each distribution. Shaded regions indicate the 68% bootstrap confidence intervals (percentiles 16–84) around the median. The AD statistics and p-values comparing both distributions are shown in the legend. The AD statistics show that galaxy mergers are preferentially located closer to filaments than non-merging galaxies, both at all radii and specifically outside the virial region. Distances to filaments are truncated at 2 Mpc in the plots for visibility, although the full distributions extend up to ∼4 Mpc.