Pseudo-Siggers dichotomy conjecture for reducts of finitely bounded homogeneous structures

Let $\mathbf{A}$ be the core of a reduct of a finitely bounded homogeneous structure. A pseudo-Siggers identity is an identity of the form

$$\alpha\circ s(x,y,x,z,y,z)=\beta\circ s(y,x,z,x,z,y),$$

where $s$ is a 6-ary polymorphism and $\alpha,\beta$ are unary polymorphisms. Pseudo-Siggers dichotomy conjecture. $\operatorname{CSP}(\mathbf{A})$ is in P if and only if $\mathbf{A}$ has such polymorphisms; otherwise, $\operatorname{CSP}(\mathbf{A})$ is NP-complete. This is described as the main conjecture in the field in the surrounding text.