Restricted CSP tractability conjecture for reducts of finitely bounded homogeneous structures

Let ${\mathbb A}$ be a reduct of a finitely bounded homogeneous structure, and let ${\mathbb B}$ be a finite structure. The restricted constraint satisfaction problem $\operatorname{RCSP}({\mathbb A},{\mathbb B})$ has ${\mathbb A}$ as its infinite template and ${\mathbb B}$ as its finite restriction. Let ${\mathbb K}_3$ be the complete graph on three vertices, let ${\mathbb L}$ be the finite structure used in the restricted pp-construction, and let rpp-construct mean restricted primitive-positive construct.

Restricted CSP tractability conjecture. If the restricted $\operatorname{CSP}$-template does not rpp-construct $({\mathbb K}_3,{\mathbb L})$, then $\operatorname{RCSP}({\mathbb A},{\mathbb B})$ is polynomial-time solvable.

The paper states that this conjecture is equivalent to the tractability conjecture above for restricted CSP templates with finite restrictions, and presents the general tractability conjecture as wide open.