Integral Prasanna–Venkatesh regulator relation for base change

Let $f$ be a normalized newform, $F$ the number field in the paper, and $f_F$ its base change. Let $\widetilde{u}_2(f_F)$ be the normalized degree-two period quantity, $\Omega_f^+$ and $\Omega_f^-$ the periods of $f$, and $R_{f,\alpha}$ the archimedean regulator. Assume $p>2k-1$, $(p,N)=1$, $(\operatorname{Reg})_p$ holds, and $(\operatorname{Min}_F)$ holds. Integral Prasanna–Venkatesh regulator relation. One has

$$\widetilde{u}_2(f_F)\sim \Omega_f^+\Omega_f^-\cdot R_{f,\alpha}.$$

The relation is presented as an integral version of the rational comparison conjectured by Prasanna and Venkatesh, identifying motivic cohomology with a Hom-space between base-change cohomology groups. The source does not state a resolution status.