Green–red balance conjecture for framed quiver mutation sequences

Let $Q$ be a framed quiver and let $v_1,v_2,\ldots$ be a mutation sequence. For each mutation index $i$, let $r_i$ denote the associated term and let $M$ be the set of relevant monomials. Green–red balance conjecture. For every $m\in M$ and every $n$, the number of indices $i\leq n$ for which $r_i=m$ and $r_i$ is green is at least the number for which $r_i=m$ and $r_i$ is red. The conjecture is presented as the condition expected to ensure that the deformed $F$-polynomial remains a polynomial; the source gives no resolution.