Universal Beilinson–Flach Euler system conjecture

Let $U$ be a sufficiently small affinoid in the half-ordinary universal deformation family, let $V_U$ be its associated representation, and let $\mathscr{D}^+_U$ be the chosen Panchishkin submodule. Assume that all classical specialisations of $U$ lie in the interpolation range under consideration. For a classical point $x\in U$ corresponding to modular forms $(f_x,g_x)$, let

$$\mathcal{BF}_\infty(f_x,g_x)\in H^1_{\operatorname{Iw}}\bigl(\mathbb{Q},V(f_x)^\ast(1)\otimes V(g_x)^\ast(1)\bigr)$$

be the Beilinson–Flach class. Universal Beilinson–Flach Euler system conjecture. There exists a global Iwasawa cohomology class

$$\mathcal{BF}_U\in H^1_{\operatorname{Iw}}(\mathbb{Q},V_U^\ast(1))$$

such that for every classical point $x\in U$, its specialisation at $x$ is $\mathcal{BF}_\infty(f_x,g_x)$, normalised compatibly with the explicit reciprocity laws. The classical Beilinson–Flach Euler system is known, but gluing these classes over the half-ordinary universal deformation family remains open; the analytic constructions cited in the source neither assume nor prove this universal Euler system.