A powerful tool for reconstructing past temperatures is based on the extent of carbonate ions in carbonate minerals with more than one heavy isotope substitution, termed carbonate clumped isotopes. The use of the clumped isotope thermometer assumes that the mineral formed under isotopic equilibrium conditions, however, some carbonate minerals can form from dissolved inorganic carbon pools that are not equilibrated. Here, we use dual clumped isotope measurements of mass 47 and mass 48 (13C18O16O - Δ47; 12C18O18O - Δ48) CO2 from gas liberated by acid digestion of carbonate minerals to constrain equilibrium clumped isotope relationships and kinetic isotope effects. In one manuscript, we present results for widely used laboratory standards that lay a strong foundation for the measurement and application of paired Δ47 and Δ48. In a second manuscript, the results from controlled inorganic calcite precipitation experiments constrain kinetic isotope effects in Δ47 and Δ48 from hydration and hydroxylation and compared to theory, and enzymatic effects are studied. Non-linear mixing effects in Δ47 and Δ48 are also determined using experiments and theory. In a third manuscript, we report Δ47 and Δ48 for amorphous calcium magnesium carbonates and transformation products, and show they are distinct from mineral equilibrium. We propose a new mechanism for disequilibrium clumped and oxygen isotope values in carbonate minerals that precipitate from an amorphous calcium carbonate precursor. Results indicate that the dissolution of an amorphous precursor may cause disequilibrium in the dissolved inorganic pool during transformation to a crystalline phase, that can impact final mineral dual clumped isotope and oxygen isotope values.