Fundamental metallicity relation used in this work. Each point corresponds to a stellar mass and star formation rate of a galaxy from a single realization of a R_nl = 5 cMpc volume at mean density at z = 6, with the color denoting its metallicity: ${\stackrel{\sim }{Z}}^j$ $\sim p_z(Z|{\stackrel{\sim }{\mathrm{SFR}}}^j,{\stackrel{\sim }{M}}_{*}^j)$ (see text for details). Stars denote the observationally estimated means in three bins for z > 6 galaxies in Curti et al. (2024) (converted from gas metalicities, see text for details), as well as the metallicity estimate of GN-z11 from Bunker et al. (2023).