Coincidence of Aronszajn null sets and heat kernel null sets

Let $G$ be a stratified Banach-Lie group with finite-dimensional commutator subgroup. An Aronszajn null set is a set null on the relevant affine lines in the Aronszajn sense, and a heat kernel null set is a set null for the heat kernel measure. Coincidence conjecture. In every such group $G$, the class of Aronszajn null sets and the class of heat kernel null sets coincide. This would extend the known equivalence in infinite-dimensional Heisenberg-like groups to stratified Banach-Lie groups with finite-dimensional commutator subgroup; the conjecture is motivated by expected broader regularity results, but remains open, with higher-step groups presenting technical difficulties.