Liu's Fundamental Lemma conjecture

Assume that $F/F_0$ is an unramified quadratic extension of $p$-adic fields for an odd prime $p$, and retain the groups $G(V_0)$ and $G(V_1)$, the symmetric space $S_n(F_0)$, and the notion of smooth transfer defined by matching regular orbital integrals. Let $K_0$ be the stabilizer of a fixed self-dual $O_F$-lattice in $V_0$. Liu's Fundamental Lemma conjecture. The characteristic function

$$\mathbf{1}_{S_n(O_{F_0})} \in C_c^\infty(S_n(F_0))$$

transfers to the pair

$$(\mathbf{1}_{K_0},0) \in C_c^\infty(G(V_0)(F_0))\times C_c^\infty(G(V_1)(F_0)).$$

This is the unit-element case of the Fundamental Lemma in Liu's setting. The source states that the conjecture remains open when $r>0$.