Explicit reciprocity conjecture for Rubin–Stark elements

Let $S:=S_\infty(k)\cup S_p(k)\cup S_{\rm ram}(L/k)$, assume the Rubin–Stark conjecture for all finite subextensions of $Lk(p^\infty)/k$, and suppose that $p$ splits completely in $k$. Let $\mathbb T_\infty$ be the corresponding Iwasawa representation, let ${\rm loc}_\Sigma$ be localization at the places in $\Sigma$, and let ${\rm Col}_v$ be the Coleman maps. Explicit reciprocity conjecture.

$$\bigwedge_{v\in\Sigma}{\rm Col}_v\bigl({\rm loc}_\Sigma(\epsilon^{S_\infty(k),\chi}_{L(p^\infty)/k,S})\bigr)=L_{p,\Sigma}^{\chi,\iota}.$$

This conjecture identifies the Coleman-map image of the Iwasawa-theoretic Rubin–Stark element with Katz's $p$-adic $L$-function. The supplied context does not establish its resolution.