The dichotomy conjecture for constraint satisfaction problems of reducts

Let $\Delta$ be a finitely bounded homogeneous structure, and let $\Gamma$ be a finite-language reduct of $\Delta$. The constraint satisfaction problem of $\Gamma$ is denoted by $\operatorname{CSP}(\Gamma)$.

Dichotomy conjecture. $\operatorname{CSP}(\Gamma)$ is either in P or NP-complete.

Complete classifications with this dichotomy were known for the empty structure, the rationals with their usual order, and the random graph. The conjecture proposes that the same P-versus-NP-complete classification holds for every finite-language reduct of a finitely bounded homogeneous structure; membership in NP is already known in this setting.