The XOP2 characterization of binary disc2,3-error

Let $\mathcal{L}={R(x,y,z)}$ be the language of ternary $3$-graph relations, and let $\text{XOP}_2$ be a proposed definition given by an infinite scheme of existential sentences. XOP2 conjecture. There exists such a definition $\text{XOP}_2$ (the “Unknown Order Property”) such that a hereditary $3$-graph property admits binary $\textnormal{disc}_{2,3}$-error if and only if it does not satisfy $\text{XOP}_2$. The source lists this among open questions and provides no resolution.