Covering fraction of pristine Lyα absorbers as a function of N_{H I} in regions C, F, and I from Figure 1, corresponding to z ∼ 5, 4, and 3 and shown in red, black, and blue, respectively. Solid lines show our high-resolution simulation, while dashed lines show a simulation with TNG100 resolution. The y-axis shows the fraction of surface area with N_{H I} greater than the value on the x-axis due to pristine gas cells with Z < 10⁻⁴ Z_⊙ in low-density regions with ﹩{\rho }_{\mathrm{dm}}\lt 5\overline{{\rho }_{\mathrm{dm}}}﹩, with ﹩\overline{{\rho }_{\mathrm{dm}}}﹩ the mean matter density at the corresponding redshift. The vertical dotted line marks the LLS threshold. In our high-resolution simulation, the covering fractions of pristine LLSs are ∼0.005, 0.01, and 0.35 at z ∼ 3, 4, and 5, respectively. In the simulation with TNG100 resolution, the covering fractions are ∼4 × 10⁻⁴, 4 × 10⁻⁴, and 0.05, respectively.