Levitt–McCammond's conjecture on intrinsically aperiodic flats

Let $X$ be a compact locally CAT(0) triangle-square complex, and let $F$ be an intrinsically aperiodic flat, meaning that $F$ does not admit a cocompact cellular action of $\mathbb{Z}^2$. Levitt–McCammond's conjecture. $F$ does not isometrically embed in $\widetilde{X}$. This conjecture concerns the obstruction posed by intrinsically aperiodic flats to biautomaticity; the supplied text does not establish its resolution.