The model-complete-core CSP dichotomy conjecture

Let $\mathbb{A}$ be a reduct of a finitely bounded homogeneous structure, and let $\mathbb{B}$ be its model-complete core. Let $\mathbb{S}$ be the finite structure defined by

$$\mathbb{S}:=(\{0,1\};\{(0,0,1),(0,1,0),(1,0,0)\}).$$

A structure pp-interprets another with parameters when the latter has a primitive-positive interpretation in the former using parameters.

Model-complete-core CSP dichotomy conjecture. One of the following holds:

1. $\mathbb{B}$ pp-interprets $\mathbb{S}$ with parameters, and consequently $\operatorname{CSP}(\mathbb{A})$ is NP-complete.
2. $\operatorname{CSP}(\mathbb{A})$ is polynomial-time solvable.

The first alternative is known to imply NP-completeness; the conjecture asserts tractability in the complementary case. The source presents this as the older dichotomy conjecture for reducts of finitely bounded homogeneous structures and relates its proposed tractability criterion to Siggers identities modulo outer embeddings.