The noncommutative $p$-adic $L$-function interpolation conjecture for elliptic curves

Let $K_\infty/K$ be a strongly admissible $p$-adic Lie extension with Galois group $G$, let $E$ be an elliptic curve, and let $\Lambda(G)$ be the Iwasawa algebra. Let $R$ be the set of rational primes ramifying infinitely in $K_\infty/K$, define

$$L_R(E/K,\tau,s)=\prod_{v\notin R}P_v(E,\tau,q_v^{-s})^{-1},$$

and, at primes $v_p$ above $p$, write

$$P_{v_p}(E,T)=(1-b_{v_p}T)(1-c_{v_p}T),\qquad b_{v_p}\in\mathbb{Z}_p^\times.$$

For an Artin representation $\tau$ of $G$, let $\tau^*$ be its dual, let $d^+(\tau)$ and $d^-(\tau)$ be the dimensions of its complex-conjugation eigenspaces, let $\varepsilon_{v_p}(\tau)$ be the local epsilon factor, and let $p^{f_\tau}$ be the $p$-part of its conductor. The interpolation conjecture. If $E$ has good ordinary reduction at all primes above $p$, then there exists $\mathfrak{L}_E\in K_1(\Lambda(G)_{S^*})$ such that $\mathfrak{L}_E(\tau)\ne\infty$ for every Artin representation $\tau$ of $G$, and

$$\mathfrak{L}_E(\tau^*)=\frac{L_R(E,\tau,1)}{\Omega_+(E)^{d^+(\tau)}\Omega_-(E)^{d^-(\tau)}}\cdot\prod_{v_p\mid p}\varepsilon_{v_p}(\tau)\cdot\frac{P_{v_p}(\tau^*,b_{v_p}^{-1})}{P_{v_p}(\tau,c_{v_p}^{-1})}\cdot b_{v_p}^{-f_\tau}.$$

This is the analogue for $K_\infty/K$ of the cited interpolation conjecture in noncommutative Iwasawa theory. The source provides no evidence that it has been resolved.