4.1 Isotope ordering in aragonitic mollusks
Clumped isotope values of our temperature-controlled A. islandicasamples consistently plot on a linear relationship with other low-temperature aragonite datapoints (Fig. 1 and 2 ; seesection 4.2 ). The absence of a consistent offset betweenA. islandica datapoints and other aragonites (+0.003 ± 0.004‰; 95% CL, see Fig. 2 and S8 ) and agreement between the linear ∆47-\(\frac{1}{T^{2}}\) dependence of the aragonitic mollusk data in this study and the regression through the complete low-temperature aragonite dataset (Fig. 1 andsection 3.1 ) strongly supports a common temperature dependence for all aragonites in this study, biogenic or inorganic, and argues against disequilibrium fractionation in aragonite precipitated inorganically or by bivalves or foraminifera (see section 3.1 ;Fig. 1 and 2 ). Our highly temperature-controlled growth experiments uniquely allow us to exclude variability in the growth environment between specimens from the same growth treatment as a driver of shell composition. Strong similarity of Δ47 values between individual A. islandica specimens grown at the same temperature thus rules out significant (95% CL) specimen-specific vital effects on the clumped isotope composition aragonitic bivalve shells (see section 3.1 ; Fig. 1 , Table 1 andS6 ). These findings corroborate measurements in calcitic mollusks showing that clumped isotope values in mollusk carbonates adhere to the same temperature relationship as other carbonates precipitated in equilibrium (except for juvenile oyster shells; Huyghe et al., 2022). Clumped isotope analyses in (fossil) mollusk shells thus provide an independent temperature proxy, allowing paleoclimatologists to disentangle the effects of variability in temperature and the hydrological cycle (as measured in δ18Ow) throughout geological history down to the seasonal timescale (e.g. Caldarescu et al., 2021; de Winter et al., 2021; Letulle et al., 2022).