The conjecture that every model of curve-excluding fields has SOP$_3$

Let $C\mathrm{XF}$ be the theory of fields excluding the curve $C$ over the base field $K_0$, and let $M$ be a model of $C\mathrm{XF}$. The property $\mathrm{SOP}_3$ is the strict order property of level $3$, while a theory is strictly $\mathrm{NSOP}_4$ if it is $\mathrm{NSOP}_4$ but not $\mathrm{NSOP}_3$. The SOP$_3$ conjecture. Every model of $C\mathrm{XF}$ has $\mathrm{SOP}_3$; equivalently, every model of $C\mathrm{XF}$ is strictly $\mathrm{NSOP}_4$. The paper proves that all models are $\mathrm{NSOP}_4$ and gives some models with $\mathrm{SOP}_3$, but the assertion for every curve $C$, base field $K_0$, and model remains open.