The p-adic Gross–Kohnen–Zagier conjecture for Big Heegner points

Let $\mathcal{R}$ be a primitive branch of a Hida family. Its Big Heegner points determine proportionality coefficients in the fraction field of $\mathcal{R}$, and let $\mathbb{S}$ denote the $p$-adic family of Jacobi forms obtained by theta lifting the Hida family. The p-adic Gross–Kohnen–Zagier conjecture. There exists a Zariski open subset of $\operatorname{Spec}(\mathcal{R})$ on which the proportionality coefficients relating Big Heegner points equal the Jacobi–Fourier coefficients of $\mathbb{S}$. This is a $p$-adic interpolation of the Gross–Kohnen–Zagier relation between Heegner points and Fourier coefficients of theta lifts; the source does not state a resolution.