Comparison of the observational SHMR in COSMOS-Web with results from various hydrodynamical simulations and the semi-empirical model UNIVERSEMACHINE. Solid lines represent the observational SHMR M_⋆,th/M_h,min, obtained from HOD fitting of mass-limited galaxy clustering measurements in COSMOS-Web. The point at 10.5 ≤ z < 14 is represented in dotted lines because it is considered less certain. The dashed and other lines represent the SHMR in the simulations computed similarly to the observations, where M_h, min is the halo mass at which 50% of halos host a central galaxy with a stellar mass above M_⋆,th. Top left: SHMR from TNG100 simulation snapshots, computed at the mean redshifts of each observational redshift range. Top right: SHMR from Horizon-AGN light-cone, calculated over the same redshift ranges as the observations, but limited to z ≤ 6. Bottom right: Same from UNIVERSEMACHINE light-cone in the COSMOS field, matching the observational redshift ranges. Bottom left: Same for high-z simulations (THESAN-1, FirstLight, OBELISK), computed from snapshots at mean redshifts from z ∼ 5 to z ∼ 12.