Signed Selmer cotorsion conjecture over the cyclotomic extension

Let $E$ be an elliptic curve over the number field $F'$, let $F$ be a finite extension satisfying the hypotheses of the paper, and let $F^{\mathrm{cyc}}$ be the cyclotomic $\mathbb{Z}_p$-extension of $F$, with $\Gamma=\operatorname{Gal}(F^{\mathrm{cyc}}/F)$. For each choice ${\vec{s}}=(s_v)_{v\in\Sigma_{\mathrm{ss}}}\in\{+,-\}^{\Sigma_{\mathrm{ss}}}$, let $X^{\vec{s}}(E/F^{\mathrm{cyc}})$ denote the Pontryagin dual of the corresponding signed Selmer group. Signed Selmer cotorsion conjecture. For all choices of ${\vec{s}}$, the $\mathbb{Z}_p[[\Gamma]]$-module $X^{\vec{s}}(E/F^{\mathrm{cyc}})$ is torsion. For an elliptic curve over $\mathbb{Q}$ with good supersingular reduction at $p$, this conjecture was proved by Kobayashi; the source notes generalizations and further progress.