Star-Crossed Labours: Checking Consistency Between Current Supernovae Compilations

We make use of model-independent statistical methods to assess the consistency of three different supernova compilations: Union3, Pantheon+ and DES 5-year supernovae. We expand the available model space of each, using Crossing Statistics, and test the compatibility of each dataset, against the other two. This is done using (I) a Flat $\Lambda$CDM fitting to, and (II) Iterative Smoothing from, one particular dataset, and determining the level of deformation by required to fit the other two. This allows us to test the mutual consistency of the datasets both within the standard model and in the case of some extended model, motivated by features present in a particular dataset. We find that, in both these cases, the data are only consistent with the point in the parameter space corresponding to zero deformation, at around a $2\sigma$ level, with the DES compilation showing the largest disagreement. However, all three datasets are still found to be consistent to within $1-2\sigma$ for some subset of the extended model space implied by the deformations.