The unitary Eisenstein embedding conjecture for cuspidal functions

Let $F$ be a non-archimedean local field with residue field $k$, let $\mathcal C$ be a curve over the ring of integers of $F$, and let $E_{\operatorname{Bun},1/2}$ be the Eisenstein map from functions on the special-fiber moduli stack to automorphic half-forms. Let $\iota_{1/2}$ be the map from half-form sections to smooth sections, and let “cuspidal functions” denote the cuspidal subspace. The unitary Eisenstein embedding conjecture. Assuming the niceness conjecture for $\operatorname{Bun}$, the composition $\iota_{1/2}\circ E_{\operatorname{Bun},1/2}$ is unitary on cuspidal functions. The conjecture predicts an isometric realization of the cuspidal spectrum in the local automorphic space; the source gives no resolution status.