Clozel–Harris–Taylor's generalized Ihara lemma for definite unitary groups

Let $\mathsf{F}^+$ be a totally real number field, let $\mathsf{F}/\mathsf{F}^+$ be a quadratic CM extension containing an imaginary quadratic field $\mathsf{K}$, and let $\mathsf{G}$ be the unitary similitude group associated to a division algebra with involution as in the setup. At a prime $p$ split in $\mathsf{K}$, choose a place $v$ of $\mathsf{F}$ above a fixed place $\wp$ of $\mathsf{K}$ above $p$, with the division algebra split at $v$. Let $K^v$ and $\mathcal{A}(K^v)$ be as defined above, let $\Lambda=\overline{\mathbb{F}}_\ell$ for $\ell\neq p$, and let $\mathbb{T}^S$ be the global Hecke algebra. An irreducible $\mathrm{GL}_n(\mathsf{F}_v)$-representation over $\Lambda$ is Whittaker-generic if it admits nonzero Whittaker coefficients. Let $\mathfrak{m}\subseteq\mathbb{T}^S$ be a non-Eisenstein maximal ideal with $\mathcal{A}(K^v)_\mathfrak{m}\neq 0$, and let $V\subseteq\mathcal{A}(K^v)_\mathfrak{m}$ be an irreducible $\mathrm{GL}_n(\mathsf{F}_v)$-submodule.

Clozel–Harris–Taylor's generalized Ihara lemma. Then $V$ is Whittaker-generic.

This is the generalized Ihara lemma proposed by Clozel, Harris, and Taylor for higher-dimensional unitary groups. The supplied material does not state whether this formulation has been proved or remains open.