The isomorphism–isometry conjecture for symplectic quandles over \mathbb{Z}_n

Let $Q$ and $Q'$ be symplectic quandles of the same dimension over the ring $\mathbb{Z}_n$. They are isomorphism–isometry conjecture. Isomorphic as quandles if and only if they are isometric as symplectic quandles.

The conjecture is motivated by the theorem that non-degenerate symplectic quandles of the same dimension over a principal ideal domain are isomorphic as quandles if and only if they are isometric. The authors report that their search for counterexamples over $\mathbb{Z}_n$ with non-prime $n$ had found none, leaving the assertion open in the stated generality.