The vanishing conjecture for the modified equivariant local epsilon term

Let $K$ be a finite extension of ${\mathbb Q}_p$, let $N/K$ be a finite Galois extension with Galois group $G$, and retain the notation $\tilde R_{N/K}$ and $K_0(\tilde\Lambda,\tilde\Omega)$ introduced above. Modified epsilon-term vanishing conjecture. Under the current assumptions,

$$\tilde R_{N/K}=0\quad\text{in }K_0(\tilde\Lambda,\tilde\Omega).$$

In the case $\chi^{\mathrm{nr}}|_{G_N}\ne 1$, this is precisely the reformulation of the preceding equivariant local epsilon-constant conjecture, while the general relationship is established in the surrounding discussion; no resolution is stated here.