Evolution of Δ χ² with metallicity or C/O ratio. The χ² values are computed by comparing 1D chemical models to the K2-18 b observations from Madhusudhan et al. (2023). The Δ χ² values represent the difference from the best-fit model. The 1D projection is obtained by selecting the lowest χ² across the other parameter dimension (metallicity or C/O). The shaded area represents the dispersion from Kzz, which has no preferred value (within 1σ), while the solid line indicates the median across Kzz values. The red line represents the Δ χ² for the best flat-line retrieval, demonstrating a confidence level of the best fit exceeding 4σ. An additional best-fit value with a 2σ uncertainty for metallicity and a lower limit at 3σ for metallicity and C/O are shown in blue, derived from a polynomial fit in log scale.