Mean angle 〈θ〉 as a function of distance to the nearest filament spine D_fil, measured using filaments identified with DisPerSE at three persistence thresholds. Red/blue/green curves show results for persistence levels labeled 1σ, 2σ, and 3σ, respectively; all filament catalogs are constructed from the same galaxy sample. Error bars indicate measurement uncertainties. The horizontal dashed line marks 〈θ〉 = 45^∘ (random orientations).