The Lemma–Flach factorisation conjecture for the $d$-region

Let $\underline{\Pi}$ be a family on $\operatorname{GSp}_4$ whose specialisations have root number $-1$, let $\underline{\sigma}$ be the accompanying $\mathrm{GL}_2$ family, and let $\operatorname{Log}_c$ be the Perrin-Riou exponential map. Let $\mathrm{LF}_{\underline{\Pi}}^{\dagger}$ be the family of Lemma–Flach classes in the indicated Selmer group. Lemma–Flach factorisation conjecture. There is an element $\mathcal C_d\in\mathcal R_{\underline{\Pi}}[1/p]$ such that

$$L_p^{(d)}(\underline{\Pi}\times\operatorname{ad}\,\underline{\sigma})^2(P,Q,Q)=\mathcal C_d(P)L_p^{(e)}(\underline{\Pi}\times\operatorname{ad}^0\,\underline{\sigma})(P,Q)\operatorname{Log}_c(\mathrm{LF}_{\underline{\Pi}}^{\dagger}).$$

The conjecture predicts that wall crossing from the $d$-region to the $e$-region is controlled by the Perrin-Riou logarithm of a Lemma–Flach class; the construction of that class is not complete, although a key step is cited in the source.