Minuscule bi-analytic Ax–Schanuel conjecture

Let $G/\mathbb{Q}_p$ be a reductive group, let $[\mu]$ be a minuscule conjugacy class of cocharacters of $G_{\overline{\mathbb{Q}}_p}$, and let $b\in G(\breve{\mathbb{Q}}_p)$ represent the unique basic class in $B(G,[\mu^{-1}])$. Let $L/\breve{\mathbb{Q}}_p([\mu])$ be a $p$-adic field. Let $\mathrm{D}$ be the space defined in the source setup, let $C$ be the completed algebraic closure, and suppose $S\subseteq\mathrm{D}_C$ is a smooth locally closed $\overline{L}$-analytic subvariety. An intersection is called exceptional according to the source's tangent-dimension condition, and a strictly special subvariety is the source's designated special subvariety. Minuscule bi-analytic Ax–Schanuel conjecture. If $Z\subseteq\mathcal{M}^{\tau}\cap S$ is an exceptional component, then $Z$ is contained in a strictly special subvariety of $\mathcal{M}^{\tau}_C$. This is the paper's main Ax–Schanuel-type claim: strictly special subvarieties are conjectured to account for all exceptional intersections, and no resolution is supplied.