The following diagram showing subclasses of the class of hereditarily semi-simple (HSS) varieties appears to have a missing variety at the place marked with a query.
(Here CP=congruence permutable, CD=congruence distributive, FI=filtral D=discriminator, FG=finitely-generated, PP=paraprimal, QP=quasiprimal.)
A non-trivial variety, V, is called mysterious if for some r, \(1\leq r<\omega\), there are 3-place terms M and \(t_ 0,...t_{r-1}\) such that the subdirectly irreducible members of V satisfy the following axioms. (a) \(M(x,y,y)=x;\) (b) \(M(x,x,y)=y;\) (c) \(t_ p(x,x,y)=y,p<r;\) (d) \(x\neq y\to\bigvee_{p<r}t_ p(x,y,z)=x.\) The main result of this note is that mysterious varieties indeed occupy the desired position in the above diagram.