Numerical resolution convergence from one representative run (L_j ≃ 10⁴³ erg s⁻¹, r_c, s = 500 pc, θ_obs = 5°). Top: Radio (z_radio, blue) and optical (z_opt, red) centroid positions as a function of the resolution multiplier relative to the fiducial 800 × 5000 grid. The filled circles pass the Gaia flux threshold; the open circles do not. The light-gray band marks the resolutions at which no synchrotron emission is produced. Bottom: Corresponding d_app values (dark-green circles). The dashed line indicates the fiducial (1×) reference.