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This paper attempts to define a generalisation of the standard Einstein condition (in conformal/metric geometry) to any parabolic geometry. To do so, it shows that any preserved involution σ of the adjoint bundle A gives rise, given certain algebraic conditions, to a unique preferred affine connection ∇ with covariantly constant rho-tensor P, compatible with the algebraic bracket on A. These conditions can reasonably be considered the generalisations of the Einstein condition, and recreate thearXiv:0705.2390v5 fatcat:nrtfhjz4avd67mxzrekqj66kb4