Dipole of the two-point correlation function ξ₁(s) for different violation scenarios. Left: ξ₁(s) for the GR case (α = β = γ = 0, blue solid) and two examples with nonzero violation parameters (red dashed and purple dashed). Right: residual difference of the dipole in the violation scenarios to the GR dipole. The horizontal dashed line at 1 marks the GR expectation. All curves assume ΔC = 0.1, M_halo = 10¹³M_⊙, and σ_v = 300 km s⁻¹. The distinct scale dependencies allow the individual equivalence principles to be constrained.