Fundamental Lemma for regular semi-simple adjoint-stable pairs

Let $V$ be a hermitian space over $E$, and let $I(x,j)$ be the number of self-dual lattices satisfying the stated stability conditions. Let $O(x,j)$ be the corresponding signed lattice-counting orbital quantity. A pair $(x,j)\in\operatorname{End}_E(V)\times V$ is regular semi-simple when $E[x]j=V$, and it is adjoint-stable when $\mathcal{O}_E[x]=\mathcal{O}_E[x^*]$. Fundamental Lemma. For every regular semi-simple and adjoint-stable pair $(x,j)$,

$$I(x,j)=O(x,j).$$

This is the lattice-counting formulation of the Jacquet–Rallis Fundamental Lemma in the even hermitian case. The source does not provide resolution evidence for this formulation.