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We characterize Cauchy data sets leading to vacuum space-times with vanishingMars-Simon tensor. This approach provides an algorithmic procedure to checkwhether a given initial data set $(\Sigma,h_{ij},K_{ij})$ evolves into aspace-time which is locally isometric to a member of the Kerr-(A)(dS) family.

Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. II. KIDs for the Kerr-(A)(de Sitter) family