The Guo–Jacquet fundamental lemma

Let $E_0=F\times F$ and let $E_1,E_2$ be quadratic extensions of $F$, with $E_3$ the third quadratic extension of $F$ in $E_1\otimes_F E_2$. Let $\alpha:(E_0,E_3)\to M_{2n}(F)$ and $\beta:(E_1,E_2)\to M_{2n}(F)$ be regular semi-simple matching pairs, and let $f$ be a spherical Hecke function in $\mathcal{H}$.

Guo–Jacquet fundamental lemma. One has

$$\pm O(\alpha,f,0)=O(\beta,f).$$

Here the two sides are the matching orbital integrals on the linear and unitary sides. The supplied source presents this as a conjecture in the unramified situation, but gives no resolution evidence.