Infinite-domain CSP dichotomy conjecture

Let $\mathfrak{B}$ be a first-order reduct of a finitely bounded homogeneous structure in a finite relational signature. The constraint satisfaction problem $\operatorname{CSP}(\mathfrak{B})$ asks whether a finite input structure admits a homomorphism to $\mathfrak{B}$. Infinite-domain CSP dichotomy conjecture. The problem $\operatorname{CSP}(\mathfrak{B})$ is either in $\mathbf{P}$ or is $\mathbf{NP}$-complete. This extends the finite-domain CSP dichotomy to the indicated class of infinite-domain templates; the source presents it as open and attributes it to earlier work.