The quarter-distance isomorphism conjecture for Moufang 2-loops

Let $L=(G,\circ)$ and $M=(G,*)$ be Moufang $2$-loops on the same set $G$ of order $n$, and define their distance by

$$d(\circ,*)=\left|\{(a,b)\in G\times G: a\circ b\ne a*b\}\right|.$$

Quarter-distance isomorphism conjecture. If $d(\circ,*)<n^2/4$, then $L$ and $M$ are isomorphic. The analogous assertion is known for groups, and the paper presents the bound as the smallest possible distance for distinct Moufang $2$-loops; no proof is given for Moufang $2$-loops.