The test function conjecture via nearby cycles

Let $Sh_{K_p}$ be the Shimura variety, let $\mathcal M_{K_p}/\mathcal O_E$ be a natural integral model, and let $R\Psi_x$ denote the nearby-cycles complex at a point $x$ of its special fiber. Let $\Phi_p$ be geometric Frobenius, $\phi_r$ the test function, and let $c(\gamma_0;\gamma,\delta)$, ${\rm O}(1_{K^p})$, and ${\rm TO}_{\delta\theta}(\phi_r)$ be the terms in the semisimple trace formula. Nearby-cycles test function conjecture. There exists a natural integral model $\mathcal M_{K_p}/\mathcal O_E$ such that

$$\sum_{x\in\mathcal M_{K_p}(k_{E_{j0}})}{\rm tr}^{\rm ss}(\Phi_p^r,R\Psi_x)=\sum_{(\gamma_0;\gamma,\delta)}c(\gamma_0;\gamma,\delta)~{\rm O}(1_{K^p})~{\rm TO}_{\delta\theta}(\phi_r),$$

where $\phi_r=p^{rd/2}\bigl(Z_{V^{E_{j0}}_{-\mu,j}}*1_{K_{p^r}}\bigr)$. The source explicitly says that some unconditional versions have been proved, but this formulation is not stated as fully resolved.