The Spi framework provides a 4-dimensional approach to investigate the asymptotic properties of gravitational fields as one recedes from isolated systems in any space-like direction, without reference to a Cauchy surface [1]. It is well suited to unify descriptions at null and spatial infinity because \( \mathcal{I} \) arises as the null cone of i°. The goal of this work is to complete this task by introducing a natural extension of the asymptotic conditions at null and spatial infinity of [2], by ‘gluing’ the two descriptions appropriately. Space-times satisfying these conditions are asymptotically flat in both regimes and thus represent isolated gravitating systems. They will be said to be Asymptotically Minkowskian at i°. We show that in these space-times the Spi group \( \mathfrak{S} \) as well as the BMS group \( \mathcal{B} \) naturally reduce to a single Poincaré group, denoted by \( {\mathfrak{p}}_{i^{{}^{\circ}}} \) to highlight the fact that it arises from the gluing procedure at i°. The asymptotic conditions are sufficiently weak to allow for the possibility that the Newman-Penrose component \( {\Psi}_1^{{}^{\circ}} \) diverges in the distant past along \( \mathcal{I} \) +. This can occur in astrophysical sources that are not asymptotically stationary in the past, e.g. in scattering situations. Nonetheless, as we show in the companion paper [5], the energy momentum and angular momentum defined at i° equals the sum of that defined at a cross-section C of \( \mathcal{I} \) + and corresponding flux across \( \mathcal{I} \) + to the past of C, when the quantities refer to the preferred Poincaré subgroup \( {\mathfrak{p}}_{i^{{}^{\circ}}} \) .
