Hiraga–Ichino–Ikeda conjecture for unipotent representations

Let $F$ be a nonarchimedean local field, let $G$ be the group of $F$-points of a reductive group, and let $P=MU$ be a parabolic subgroup with Levi factor $M$. Let $\mathcal O=X_{\mathrm{unr}}(M)\pi$ be the orbit of a square-integrable-modulo-centre representation $π$ of $M$ under unitary unramified twists, and let $(\phi_\pi,\rho_\pi)\in\Phi_e(M)$ be its enhanced $L$-parameter. Write $\operatorname{Ad}_{G^\vee,M^\vee}$ for the adjoint representation of ${}^LM$ on $\operatorname{Lie}(G^\vee)/\operatorname{Lie}(Z(M^\vee)^{\mathbf W_K})$, and let $\psi$ and the Haar measures be normalized as specified above. Hiraga–Ichino–Ikeda conjecture. The Plancherel density at $I_P^G(\pi)$ is

$$c_M\dim(\rho_\pi)\left|Z_{(G/Z(G)_s)^\vee}(\phi_\pi)\right|^{-1}\left|\gamma\left(0,\operatorname{Ad}_{G^\vee,M^\vee}\circ\phi_\pi,\psi\right)\right|\,\mathrm d\mathcal O(\pi),$$

where $c_M\in\mathbb R_{>0}$ is independent of $F$ and $\mathcal O$; moreover, with these Haar-measure normalizations, $c_M=1$. This is the Plancherel-density formula predicted by the Hiraga–Ichino–Ikeda conjecture; in the stated setting it is presented as a conjectural refinement of the local Langlands correspondence, and no resolution is supplied in the source.