Spectral-index radial profiles computed from images convolved with circular Gaussian beams of different sizes (FWHM = 20, 25, 30, 35, and 40 μas), using the GMVA 2018 3.5 mm and EHT 2018 1.3 mm images. This figure illustrates the impact of beam size on the radial spectral index, highlighting how intermediate smoothing preserves the ring morphology while enabling a robust comparison between the two frequencies.