Compatibility conjecture for Mazur–Rubin local constants and epsilon constants

Let $p$ be an odd prime, let $L$ be a finite extension of $\mathbb Q_p$, and let $T_1$ and $T_2$ be symplectic self-dual $\mathcal O_L$-representations of $G_{\mathbb Q_p}$. Put

$$V_i=T_i\otimes_{\mathbb Z_p}\mathbb Q_p\qquad (i\in\{1,2\}),$$

and suppose that each $V_i$ is de Rham and that $T_1$ and $T_2$ are residually symplectically isomorphic. Let $\hat{\varepsilon}_p(V_i)$, $\Gamma(V_i)$, $\varepsilon_p(V_i)$, and $\delta_p(T_1,T_2)$ be the local invariants defined in the paper. Compatibility conjecture for local constants.

$$\frac{\hat{\varepsilon}_p(V_1)}{\hat{\varepsilon}_p(V_2)}:=\frac{\Gamma(V_1)\varepsilon_p(V_1)}{\Gamma(V_2)\varepsilon_p(V_2)}=(-1)^{\delta_p(T_1,T_2)}.$$

This conjecture seeks to identify the ratio of normalized local epsilon constants with the Mazur–Rubin arithmetic local constant. The supplied text mentions partial results of Mazur–Rubin and Nekovář in related settings but gives no resolution of the proposed statement.