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\[{R_{13}} = \left( {\frac{{\delta _{wrg - VPDB}^{13}}}{{1000}} + 1} \right) \times R_{13}^{VPDB}\]     and similar equations for $R_{17}$ and $R_{18}$. The reference gas ratios are $R_{13}^{VPDB}$ = 0.0112372 (reference), $R_{17}^{VSMOW}$ = 0.0004023261 (reference) and $R_{18}^{VSMOW}$ = 0.0020052 (reference).  Similarly the R47* $R_{47}^{*}$  ratio for a sample corresponding to a stochastic distribution of the isotopes is given by: \[R_{47}^* = 2 \cdot R_{13}^{sam} \cdot R_{18}^{sam} + 2 \cdot R_{18}^{sam} \cdot R_{17}^{sam} + R_{13}^{sam} \cdot {\left( {R_{17}^{sam}} \right)^2}\]  (5)  with R13, R17 $R_{13}$, $R_{17}$  and R18 $R_{18}$  determined using equation 4 and the measured δ13C, δ17O $\delta^{13}C$, $\delta^{17}O$  and δ18O $\delta^{18}O$  values for the sample. Substitution of R47 $R_{47}$  (equation 2) and R47* $R_{47}^{*}$  (equation 5) into equation 1 allows determination of Δ47. $\Delta_{47}$.  Evaluation of Δ48 $\Delta_{48}$  and Δ49 $\Delta_{49}$  follows the same steps as above. The complete data reduction algorithm and it’s implementation in a Mathematica program for data obtained on the MIRA mass spectrometer is included in the supplementary information. Finally, using the method outlined by Dennis et al. (2011) and the heated and water equilibrated gas standards we determine a transfer function between measurements made on the local scale with reference to the mass spectrometer working reference gas the absolute reference frame (ARF). All the results are reported with respect to the ARF. The full data set including results reported on both the local and ARF scales are included with the supplementary information.  (iii) Temperature estimation using Δ47  Using the clumped isotope composition of carbonate minerals as a geothermometer is a relatively immature technique. Of particular importance is the lack of agreement on the calibration between the deviation from a stochastic distribution of the isotopes and temperature. There exists a large number of calibrations with varying degrees of sensitivity. Moreover, most of these calibrations have been made over a restricted range of temperatures based on the collection of biogenic carbonates from environments with known temperature (e.g. references). More recently calibrations have become available for inorganically precipitated calcites. However these have not served to resolve the origin of the differences.