Finite Mal'tsev embedding conjecture for finite-domain predicates

Let $P$ be a predicate over a finite domain. An infinite Mal'tsev embedding of $P$ is a Mal'tsev embedding into an infinite structure, while a finite Mal'tsev embedding is a Mal'tsev embedding into a finite structure. The non-redundancy of $P$ measures the maximum number of constraints in an irredundant instance relative to its size.

Finite Mal'tsev embedding conjecture. Any predicate over a finite domain with an infinite Mal'tsev embedding also has a finite Mal'tsev embedding. In particular, any predicate with an infinite Mal'tsev embedding has linear non-redundancy.

This conjecture would unify the finite and infinite Mal'tsev-embedding approaches to classifying predicates with linear or near-linear non-redundancy. The paper identifies this classification as a central open question, and the conjecture is presented as a direction for future investigation.