The abundance conjecture for punctual D0-brane moduli

Let $Y$ be a reduced quasi-projective variety over $\mathbb{C}$. Let $\mathfrak M^{0^{A\!z^f}_{p}}_r(Y)$ be the moduli stack of punctual D0-branes of rank $r$ on $Y$. The abundance conjecture. Any birational model $Y'\to Y$ of and over $Y$ factors through an embedding

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

for $r$ sufficiently large. This would place arbitrary birational models inside a moduli stack of punctual D0-branes, extending the cited D-brane resolutions of ADE surface singularities and conifolds; its general validity remains open.