Perrin-Riou's integral Iwasawa-theoretic conjecture for crystalline representations

Let $K_\infty/K$ be the cyclotomic extension, let $T$ be a $\mathbf{Z}_p$-lattice in a crystalline representation $V$ of $G_K$, and let $\Lambda$ be the relevant Iwasawa algebra. Define the Iwasawa determinant line $\Delta_{\mathrm{Iw}}(K_\infty/K,T)$ and the rank-one module

$$\Lambda_{V,K_\infty/K}=\{f\in\widehat{\mathcal{O}}_{K^{\mathrm{nr}}}\widehat{\otimes}_{\mathbf{Z}_p}\Lambda\mid \sigma(f)=a_{V,K}f\},$$

where $a_{V,K}\in\mathbf{Z}_p^\times$ is the element defined in the source. Let $\delta_{V,K_\infty/K}:\Delta_{\mathrm{Iw}}(K_\infty/K,V)\xrightarrow{\sim}\Lambda_{V,K_\infty/K}\otimes_{\mathbf{Z}_p}\mathbf{Q}_p$ be the canonical trivialization.

$C_{\mathrm{Iw}}(K_\infty/K,V)$. The canonical trivialization satisfies

$$\delta_{V,K_\infty/K}\bigl(\Delta_{\mathrm{Iw}}(K_\infty/K,T)\bigr)=\Lambda_{V,K_\infty/K}.$$

This is the integral version of Perrin-Riou's conjecture $\delta_{\mathbf{Z}_p}(V)$, refining the rational Iwasawa-theoretic trivialization for crystalline representations. The supplied text does not state whether it has been resolved.