The D0-brane resolution conjecture for singularities

Let $Y$ be a reduced quasi-projective variety over $\mathbb{C}$, and let $\rho:Y'\to Y$ be a resolution of the singularities of $Y$. Let $\mathfrak M^{0^{A\!z^f}_{p}}_r(Y)$ denote the moduli stack of punctual D0-branes of rank $r$ on $Y$. D0-brane resolution conjecture. Any such resolution factors through an embedding

$$Y'\hookrightarrow\mathfrak M^{0^{A\!z^f}_{p}}_r(Y)$$

for $r$ sufficiently large. This is presented as a consequence of the abundance conjecture and the known ADE example, but no general proof or resolution status is supplied.