Harris–Viehmann conjecture for non-basic local Shimura varieties

Assume that $G$ is quasi-split and let $(G,[b],\{\mu\})$ be a non-basic local Shimura datum. Let $L$ be a Levi subgroup, assume that $J_b$ is an inner form of a Levi subgroup contained in $L$, and let $P$ be the corresponding parabolic subgroup with Levi factor $L$. For each $\{\mu'_L\}\in I_{b,\{\mu\},L}$, let $H^{\bullet}((L,[b]_L,\{\mu'_L\}))[\rho]$ be the associated Grothendieck-group element. Harris–Viehmann conjecture. In ${\rm Groth}(G(F)\times W_{E_{\{\mu\}}})$,

$$H^{\bullet}((G,[b],\{\mu\}))[\rho]=\operatorname{Ind}^{G(F)}_{P(F)}\left(\sum_{\{\mu'_L\}\in I_{b,\{\mu\},L}}H^{\bullet}((L,[b]_L,\{\mu'_L\}))[\rho]\right).$$

The conjecture proposes an inducing formula for cohomology in the non-basic case, generalizing the expected behavior from Levi subdata. The source explicitly notes substantial scepticism and that even the precise prediction may need modification.