Homotopy kinematic algebras at null infinity

We present the first formulation of a homotopy algebra adapted to a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mi>r</a:mi> </a:math> expansion near future null infinity ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi mathvariant="script">I</c:mi> <c:mo>+</c:mo> </c:msup> </c:math> ). 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mi mathvariant="script">I</f:mi> <f:mo>+</f:mo> </f:msup> </f:math> . 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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi mathvariant="script">I</i:mi> <i:mo>+</i:mo> </i:msup> </i:math> .