Splitting conjecture for set-theoretic Yang–Baxter homology of Rump right quasigroups

A Rump right quasigroup is a set equipped with the right-quasigroup structure arising in Rump's framework for set-theoretic solutions of the Yang–Baxter equation. Its set-theoretic Yang–Baxter homology has normalized and degenerate parts. Splitting conjecture. The set-theoretic Yang–Baxter homology of any Rump right quasigroup splits into the normalized and degenerate parts.

This would extend the observed distinction between normalized and degenerate Yang–Baxter homology, including examples where torsion occurs in the set-theoretic or normalized theory but not in rack or quandle homology. The supplied material gives no resolution, so the conjecture remains open.