A $p$-adic Birch and Swinnerton-Dyer formula for the anticyclotomic Heegner element

Let $z^{\rm Hg}$ be the $\Lambda$-adic Heegner element, let $\mathcal D$ be the derived descent map, let ${\rm Eul}_S$ be the product of Euler factors at the finite places in $S$, and let ${\rm Reg}^{\rm Boc}$ be the derived Bockstein regulator. Anticyclotomic Heegner-element conjecture. There exists $u\in\mathbb Z_p^\times$ such that

$$\mathcal D(z^{\rm Hg})=u\cdot {\rm Eul}_S\cdot\#\text{\russ\char88}(E/K)[p^\infty]\cdot {\rm Tam}(E/K)\cdot {\rm Reg}^{\rm Boc}.$$

This is suggested by the explicit interpretation of the derived leading-term conjecture together with the Birch and Swinnerton-Dyer formula. The source does not prove this equality and explicitly allows an unspecified $p$-adic unit.