The finitely bounded homogeneous CSP dichotomy conjecture

Let $\mathbb A$ be a CSP template that is a first-order reduct of a countable finitely bounded homogeneous structure $\mathbb B$. Let $\operatorname{Pol}(\mathbb A)$ denote the polymorphism clone of $\mathbb A$, let $\mathscr P$ be the clone of projections, and let $\operatorname{CSP}(\mathbb A)$ denote the constraint satisfaction problem for $\mathbb A$.

Finitely bounded homogeneous CSP dichotomy conjecture. Exactly one of the following holds: either $\operatorname{Pol}(\mathbb A)$ has a uniformly continuous minion homomorphism to $\mathscr P$ and $\operatorname{CSP}(\mathbb A)$ is NP-complete, or $\operatorname{Pol}(\mathbb A)$ has no uniformly continuous minion homomorphism to $\mathscr P$ and $\operatorname{CSP}(\mathbb A)$ is in P.

This conjecture extends the finite-domain CSP dichotomy to first-order reducts of countable finitely bounded homogeneous structures. The surrounding discussion presents it as a modern formulation incorporating recent progress; the supplied text does not establish whether the full statement is resolved.