Dimitrov-Wan genus stability conjecture for ordinary algebraic-geometric towers

Let $K_{\infty}/K$ be a $p$-adic Lie tower, with Galois group $G_{\infty}$ of dimension ${\rm \dim}(G)$, arising from an algebraic-geometric $p$-adic representation. Assume the tower is ordinary, and let $g_n$ denote the genus of $K_n$.

Genus stability conjecture. There is a polynomial $G(x)\in\mathbb{Q}[x]$ of degree at most ${\rm \dim}(G)+1$, depending on the tower, such that for all sufficiently large $n$,

$$g_n=G(p^n).$$

This is a stronger genus-stability prediction for ordinary algebraic-geometric towers. The source reports substantial progress by Joe Kramer-Miller and says that the number-field discriminant analogue has been proved by James Upton; it does not state that the conjecture itself is solved.