Illustration of the factors influencing the generation of initial conditions in our simulations. The plot shows Δ² as a function of wavenumber, highlighting the upper limit of Δ² < 0.05 for appropriate 3LPT application. The red-shaded area indicates the resolution limit for k_cross (94.78, marked by the grey dotted line). If the threshold falls within this region, the simulation can begin at the corresponding redshift. Power spectra are displayed for two simulations (blue and orange) at different redshifts (solid vs. dashed lines), identifying the earliest redshift where k_cross > k_limit. This criterion determines the starting redshift. For the FCT model, this condition applies at z ∼ 1200.