Wuthrich's μ–λ conjecture for fine Selmer groups

Let $E/\mathbb{Q}$ be an elliptic curve, let $p$ be a prime of good reduction, and let $\mathcal{R}_{p^\infty}(E/\mathbb{Q}_{\operatorname{cyc}})$ be the fine Selmer group over the cyclotomic $\mathbb{Z}_p$-extension. Wuthrich's μ–λ conjecture. For all but finitely many such primes $p$,

$$\mu=0\qquad\text{and}\qquad \lambda=\max\{\operatorname{rank}E(\mathbb{Q})-1,0\}.$$

This is the source's reformulation of Wuthrich's conjecture; it is open in general, and the source proves only a conditional implication in rank zero.