A framework for triple oxygen isotopes in speleothem paleoclimatology

•New framework for interpreting triple oxygen isotope variability in speleothems.•New assessment of triple oxygen isotope fractionation between water and carbonate.•Data in Δ′17O vs. δ′18O space provide a novel assessment of within-cave kinetics.•Within-cave kinetics did not drive δ18O variability in western USA speleothems.•Reconstructed parent waters define a climate-driven slope of 0.5249 ± 0.0004.