The explicit Brumer–Stark unit conjecture via Shintani integrals

Let $F$ be a totally real field, let $H/F$ be a finite abelian CM extension, and let $\mathfrak p$ split completely in $H$. For a prime ideal $\mathfrak b$ prime to the prescribed modulus, let $\sigma_{\mathfrak b}\in G$ be its Frobenius and let $u_p(\mathfrak b)^{\mathrm{an}}\in F_p^*$ be the explicitly defined multiplicative-integral expression. Let $u_{\mathfrak p}$ be the Brumer–Stark unit. Explicit Brumer–Stark unit conjecture. One should have

$$\sigma_{\mathfrak b}(u_{\mathfrak p})=u_p(\mathfrak b)^{\mathrm{an}}\quad\text{in }F_p^*.$$

The formula is intended to compute all conjugates of the Brumer–Stark unit and has computational applications to explicit class field theory. The source gives no resolution status.