Validation of a compact soliton core in an idealized merger. Radial density profile of the simulated core (red points) compared to the analytic soliton solution (blue line; fitted r_c = 2.32 in code units). Both axes are shown in code units; the corresponding physical scaling for m₂₂ = 2 is given in Section 4 (yielding r_c ≃ 51 pc and M_c ≃ 7.8 × 10⁸ M_⊙). The deviation at large radii reflects unrelaxed merger debris and finite-box/periodic-boundary effects and does not affect the inner soliton core relevant for our analytic estimates.