3 problems

Smallness equivalence conjecture. A unital pseudoalgebra $\operatorname{Diff} A$ is small if and only if $A$ is a small $X^{cop}$-simple algebra.

Six-vertex infinite-dimensionality conjecture. The algebra $\mathcal E_G$ is infinite-dimensional if and only if $G$ contains a subgraph isomorphic to one of the graphs shown in Fi…

Finite-dimensionality conjecture. Every motive is finite-dimensional.