Assess graduate-level understanding of stable isotope fractionation principles (equilibrium vs. kinetic effects, fractionation factors, isotopic notation δ), their temperature and environmental controls, laboratory and diagenetic influences, and applications to paleoclimate proxies (δ18O, δ2H, δ13C, clumped isotopes). Include conceptual explanations, quantitative calculations (fractionation/temperature conversions, mixing scenarios), and critical evaluation of proxy limitations and uncertainties.