The Iwasawa-theoretic Rubin–Stark congruence conjecture

Let $K_\infty/k$ be the relevant $mathds{Z}_p$-extension with Galois group containing $\Gamma$, let $\Sigma$ and $T$ be the prescribed sets of places, and let $V'\setminus V=W$ have cardinality $e$. Assume that the $p$-part of the Rubin–Stark conjecture holds at every finite layer, so that the norm-coherent family $\varepsilon_{K_\infty/k,\Sigma,T}$ is defined. Write $I_\Gamma$ for the augmentation ideal of the relevant Iwasawa algebra. Iwasawa-theoretic Rubin–Stark congruence conjecture. One has

$$\varepsilon_{K_\infty/k,\Sigma,T}\in I_\Gamma^e\cdot\bigcap\nolimits^r_{\mathds{V}}U_{K_\infty,\Sigma,T}.$$

This is a higher-order congruence prediction for norm-coherent Rubin–Stark elements, measuring the vanishing forced by the additional places $W$. The source does not state a resolution.