Stoll's finite-subscheme conjecture for Chabauty–Coleman loci

Let $X$) be a smooth projective curve of genus $g\geq2$ whose Jacobian has Mordell–Weil rank at most $g-2$. Let $U_1^p$ denote the abelianisation of the fundamental group of $X_{\overline{\mathbb Q}}$. Stoll's conjecture. There is a finite subscheme $Z\subset X$, defined over $\mathbb Q$, such that

$$X(\mathbb Q_p)_{U_1^p}\subseteq Z(\mathbb Q_p)$$

for all primes $p$ in a set of Dirichlet density $1$. Because $Z$ is finite and defined over $\mathbb Q$, $Z(\mathbb Q_p)$ consists only of algebraic points. The conjecture strengthens the expectation that the abelian non-abelian Chabauty loci contain only algebraic points by requiring one finite subscheme, independent of $p$, to interpolate them; the source notes that its formulation differs slightly from Stoll's original result.