Schematic illustration of the dipole contributions. LPI (green): oscillatory shape with a decaying envelope, reflecting the BAO wiggles of ξ₀(s) modulated by 1/s² from the potential gradient. LLI (red): negative, peaked at small separations and decaying as ∼1/s, representing ﹩{\xi }_{1}^{{\rm{LLI}}}\propto -\frac{\gamma }{{H}_{0}}\frac{{\sigma }_{v}}{s}{\xi }_{0}(s)﹩. WEP (orange): similar to LPI but drawn with an asymmetry to indicate that the sign and amplitude depend on the composition difference ΔC; in reality its functional form is identical to LPI up to a constant factor. All curves are schematic and not to scale; they are intended to highlight the distinct anisotropic patterns produced by each violation.