Homotopy kinematic algebras at null infinity

We present the first formulation of a homotopy algebra adapted to a $1\mathrm{/}r$ expansion near future null infinity (${\mathcal{I}}^{+}$). Focusing on self-dual Yang-Mills theory in Bondi coordinates, we demonstrate that imposing the homotopy algebra relations naturally yields the physically consistent fall-off behavior of the fields near ${\mathcal{I}}^{+}$. Furthermore, we employ this framework to systematically construct kinematic algebras, uncovering novel infinite families of such algebras that satisfy the Jacobi identity on slices near ${\mathcal{I}}^{+}$.