Fractional-polymorphism classification conjecture for homogeneous reducts

Let $\Gamma$ be a valued structure with finite signature such that

$$\operatorname{Aut}(\Gamma)=\operatorname{Aut}(\mathfrak{B})$$

for some reduct $\mathfrak{B}$ of a countable finitely bounded homogeneous structure. A pp-construction is the primitive-positive construction notion used in the paper, and $\operatorname{VCSP}(\Gamma)$ denotes the valued constraint satisfaction problem for $\Gamma$.

Fractional-polymorphism classification conjecture. If $(\{0,1\};\operatorname{OIT})$ has no pp-construction in $\Gamma$, then $\operatorname{VCSP}(\Gamma)$ is in $\operatorname{P}$.

Otherwise, the source states that $\operatorname{VCSP}(\Gamma)$ is already known to be NP-complete. Thus the conjecture would give a full P-versus-NP-complete classification for finite-signature valued structures with the stated homogeneous-reduct automorphism group.