Kato's local epsilon conjecture

Let $(R,T,\zeta)$ be a triple as in the paper's setup, where $T$ is an $R$-representation of $G_{\mathbb Q_p}$ and $\zeta$ is a $\mathbb Z_p$-basis of $\Gamma(\overline{\mathbb Q}_p,\mathbb Z_p(1))$. Let $\Delta_R(T)$ be the determinant module defined there. Kato's local epsilon conjecture. There exists a unique compatible family of isomorphisms

$$\varepsilon_{R,\zeta}(T):\mathbf{1}_R\overset{\sim}{\longrightarrow}\Delta_R(T)$$

for all such triples, satisfying base-change compatibility, multiplicativity in exact sequences, the change-of-basis formula for $\zeta$, the stated duality commutative diagram, and agreement with the de Rham epsilon-isomorphism for every de Rham triple $(L,V,\zeta)$. This is Kato's proposed foundational compatibility conjecture for local epsilon-isomorphisms. The supplied text gives no resolution status.