5 problems

Binary-invariants conjecture. Among minimal bounded width algebras, $\mathbb{A}$ is determined up to term equivalence by $\operatorname{Inv}_2(\mathbb{A})$.

Recursive subalgebra conjecture. The set

Minority-pair conjecture. If

Semilattice-like terms conjecture. Every bounded width algebra has terms $w,s$ satisfying these identities.

Nicer-terms conjecture. There are even nicer terms satisfying identities with a clear relationship to majority and semilattice algebras.