Perrin-Riou's Heegner point main conjecture for multiplicative primes

Let $K$ be an imaginary quadratic field, let $K_\infty$ be the relevant anticyclotomic extension, and let $\Lambda$ be its Iwasawa algebra. Let $\mathfrak{X}$ denote the relevant Pontryagin-dual Selmer module, let $\check{S}_p$ be the inverse-limit Selmer group with the stated local conditions, and let $\mathbf{z}_\infty$ be the compatible system of Heegner classes. Write $\mathfrak{X}_{\rm tors}$ for the $\Lambda$-torsion submodule of $\mathfrak{X}$. Perrin-Riou's Heegner point main conjecture. The modules $\mathfrak{X}$ and $\check{S}_p$ both have $\Lambda$-rank one, and

$${\rm char}_\Lambda(\mathfrak{X}_{\rm tors})={\rm char}_\Lambda\bigl(\check{S}_p/\Lambda\mathbf{z}_\infty\bigr)^2.$$

This is described as a natural extension of Perrin-Riou's Heegner point main conjecture to multiplicative primes $p$; in the split multiplicative case, it is viewed as a primitive of the preceding equivalence. The supplied text does not establish the assertion or give a resolution status.