Conjecture 8.1 on finite Mal’tsev extensions
For every fixed arity , every -ary constraint-satisfaction problem having a Mal'tsev extension has linear non-redundancy; equivalently, its non-redundancy is in the relevant instance-size parameter .
References
Primary source
Additional references
- The Reach of Abelian Covers in Hypergraphs — arXiv — Joshua Brakensiek, Venkatesan Guruswami, Aaron Putterman
Progress summary
A September 2026 paper advances the conjecture from arity two to arity three, but does not resolve it.
The conjecture seeks near-optimal non-redundancy consequences for finite Mal’tsev extensions beyond the previously known arity-two setting. The latest paper reports progress for -uniform hypergraphs and corresponding arity-three constraint-satisfaction consequences.
September 2026 hypergraph-cover advance
Joshua Brakensiek, Venkatesan Guruswami, and Aaron Putterman report that Abelian and Catalan covers are equivalent for -uniform hypergraphs, extending the relevant consequences to arity three. Their result advances, but does not fully settle, Conjecture 8.1; the mathematical claim is unverified here.
Current status (as of September 2026): The conjecture remains open; the reported equivalence of Abelian and Catalan covers gives new arity-three consequences, but no complete resolution is recorded.
Solutions 0
No solutions have been posted yet.