Arithmetic Fundamental Lemma for unitary Lie algebras

Let $\mathfrak{s}(E_0)$ be the symmetric Lie algebra and let $\mathfrak{u}(J_1)$ be the Lie algebra of the odd unitary group. Let $Ω(y)$ and $\partial O_y$ denote the transfer factor and derivative of the orbital integral, and let $\mathrm{Int}(x)$ be the intersection number for an artinian element. Arithmetic Fundamental Lemma. For any $y\in\mathfrak{s}(E_0)_{\mathrm{rs}}$ matching an artinian element $x\in\mathfrak{u}(J_1)$,

$$Ω(y)\partial O_y(1_{\mathfrak{s}(\mathcal{O}_{E_0})})=-\mathrm{Int}(x)\log(q).$$

This is the Lie algebra version of the Arithmetic Fundamental Lemma. The source restricts to artinian elements because the intersection product was defined only in that case, and gives no resolution status.