Generalized μ=0 conjecture for fine Selmer groups

Let $p$ be a prime number, let $F$ be a number field, let $\mathcal{O}$ be the ring of integers of a finite extension of $\mathbb{Q}_p$, and let $S$ be a finite set of primes of $F$ containing the primes above $p$. Let

$$\rho:\operatorname{G}_{F,S}\longrightarrow \operatorname{GL}_n(\mathcal{O})$$

be an integral Galois representation. The generalized fine-Selmer $\mu=0$ conjecture. Its fine-Selmer $bc$-invariant satisfies

$$\mu^{\operatorname{fn}}(\rho)=0.$$

This generalizes the elliptic-curve case to arbitrary integral Galois representations; the supplied text presents it as expected and gives no resolution.