The procedure for incorporating the low- and high-density inputs into the construction of the constrained GP bridge. The blue dashed lines correspond to the samples of the fractal EoSs together with their diffused counterparts represented by purple solid lines. The two colored bands correspond to the low- and high-density limits from the chiral-EFT and pQCD EoSs. The fractal EoS is constructed from two endpoints, β_L and β_H, obtained from the sampled chiral-EFT and pQCD EoSs at the corresponding densities n_L = 2 n_s and n_H = 30 n_s. The diffusion is then performed over the broader density range [0.34,  40] n_s to ensure a smooth transition of ﹩{c}_{s}^{2}﹩ to both limits.