Formally proper Artin stack conjecture on integral étale cohomology

Let $K$ be a finite extension of $\mathbb Q_p$, let $\mathcal O_K$ be its ring of integers, and let $\mathpzc X$ be a smooth formally proper Artin stack over $\mathcal O_K$. Let $\widehat{\mathpzc X}$ denote its formal completion, and let $\Upsilon_{\mathpzc X}$ be the comparison map. Formally proper Artin stack conjecture.

$$\Upsilon_{\mathpzc X}\colon R\Gamma_{\mathrm{\acute et}}(\mathpzc X_C,\mathbb F_\ell)\longrightarrow R\Gamma_{\mathrm{\acute et}}(\widehat{\mathpzc X}_C,\mathbb F_\ell)$$

is an equivalence for any prime $\ell$. This is a stronger comparison statement than the rational Hodge-proper prediction and is intended to connect algebraic and formal étale cohomology under formal GAGA. It remains conjectural in the supplied text.