Gross's leading term conjecture

Let $(H/F,S,T,(v_i)_i,(w_i)_i)$ be as above, let $K/F$ be a finite abelian extension unramified outside $S$ with $H\subset K$ and torsion-free $\mathcal{O}_{K,S,T}^{\times}$, and put $G=\operatorname{Gal}(K/F)$. Let $I_H'=I_{\operatorname{Gal}(K/H),G}$ and $D'=\prod_{v\in V}I_{G_v,G}$ in $\mathbb{Z}[G]$, and let $R_{H/F,S,T,G}$ be the usual regulator. Gross's leading term conjecture.

$$\Theta_{K,S,T}\equiv R_{H/F,S,T,G}(\epsilon_{H,S,T,V})\pmod{I_H'D'}.$$

This refines Gross's original leading term conjecture through Rubin–Stark elements and regulator maps. The source gives no resolution status.