Geometric Verdier duality for pro-étale cohomology of Stein rigid analytic varieties

Let $C$ be the base field, let $X$ be a smooth Stein rigid analytic variety over $C$, connected and of dimension $d$, and write $\mathrm R\Gamma_{\operatorname{pro\acute{e}t}}(X,\mathbf{Q}_p(j))$ and $\mathrm R\Gamma_{\operatorname{pro\acute{e}t},c}(X,\mathbf{Q}_p(j))$ for pro-étale cohomology complexes with and without compact support. Let $\mathrm R\operatorname{Hom}_{\mathrm{VS}}$ denote derived Hom in the category of vector spaces. Geometric Verdier duality conjecture. There is a natural quasi-isomorphism

$$\mathrm R\Gamma_{\operatorname{pro\acute{e}t}}(X,\mathbf{Q}_p(j))\simeq \mathrm R\operatorname{Hom}_{\mathrm{VS}}\bigl(\mathrm R\Gamma_{\operatorname{pro\acute{e}t},c}(X,\mathbf{Q}_p(d+1-j))[2d],\mathbf{Q}_p(1)\bigr).$$

The statement is explicitly proposed as a geometric duality result in arbitrary dimension after computations that ignore functional-analytic topology. Its validity, including the omitted topological issues, remains open in the supplied text.