Fullness conjecture for points of type $S_a(X)$

Let $X$ be a smooth projective variety defined over a number field, of dimension $n$, and let $S_a(X)$ denote the set of points of type $S_a(X)$. Let $a\geq N$ be a real number. Fullness conjecture for points of type $S_a(X)$. The set of points of type $S_a(X)$ is full in $X(\mathbb{C})$. This conjecture proposes that points satisfying the paper's transcendental Liouville condition of type $S_a(X)$ are plentiful on every such variety. The supplied text does not provide evidence that the conjecture has been resolved.