Homotopy kinematic algebras at null infinity

We present the first formulation of a homotopy algebra adapted to a $1/r$ 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 $\mathcal{I^+}$.