Supporting information for "Magnesium isotopes archive the initial carbonate abundances of metasedimentary rocks prior to thermal decarbonation"

The supporting information contains five supplementary texts, five figures, and seven tables.
In this revised version, we added a new supplementary text (Text S5) that provided details of the bootstrap resampling method used in this study. We also added a new figure (Fig. S5) which indicated the Mg isotopic variations along with Mg/Ca ratios of compiled global carbonatesalso, and updated the Fig. S4 with considering the errors from bulk δ26Mg, ICAs and the uncertainty arising from the scattering of dataset. In the revised Table S5, δ26Mg for initial carbonates and their errors were listed. In addition to the changes noted above, other typos and editorial errors have been corrected.