The refined non-commutative main conjecture for an elliptic curve

Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$, let $K=\mathbb{Q}(E(p))$, and let $G$ be its relevant Galois group, assumed to have no element of order $p$. For a field $K\in\mathcal{F}$ unramified outside $\Sigma$, let $X(E/K)$ be the dual of the $p$-primary Selmer group, and let $M=h^1(E)(1)$. The refined elliptic-curve main conjecture. Under these conditions, $X(E/K)\in\mathfrak{M}_{S^*}(G)$, and there exists $\mathcal{L}=\mathcal{L}(E)\in K_1(\Lambda_A(G)_{S^*})$ whose Artin-character specializations have the stated leading-term formula at $T=0$, and whose boundary is $[\Lambda_A(G)\otimes_{\Lambda(G)}X(E/K)]$. This is the elliptic-curve case of the refined non-commutative main conjecture, combining complex and $p$-adic regulators, periods, leading $L$-values, and local Euler factors.