The non-trivially valued mutation-periodicity conjecture

Let $Q$ be a valued quiver, let $\Delta_Q^2$ be the associated ice quiver, and let $\boldsymbol{\mu}_{\sqrt l}$, $\boldsymbol{\mu}_l$, and $\boldsymbol{\mu}_l^3$ be the mutation operations defined in the paper. The cited corollaries establish mutation-periodicity properties for trivially valued $Q$.

The non-trivially valued mutation-periodicity conjecture. Corollary

$$, and consequently Corollaries$$

and

$$and Theorem$$

, also hold when $Q$ is non-trivially valued.

The claim is motivated by experiments and extends the paper's mutation-periodicity results beyond the trivially valued case; the source gives no proof or resolution.