Transitivity conjecture for quantum R-matrices with signs

Let $R$ be a solution of the quantum Yang–Baxter equation (QYBE). Let $\boldsymbol{\epsilon}=(\epsilon_{i,j})_{1\le i,j\le n}$ be a transitive $n\times n$ matrix with $\epsilon_{i,j}\in\{1,-1\}$, and define

$$\mathbf R^{(\boldsymbol{\epsilon})}:=(R_{1,2n}^{(\epsilon_{n,1})}\cdots R_{n,2n}^{(\epsilon_{n,n})})(R_{1,2n-1}^{(\epsilon_{n-1,1})}\cdots R_{n,2n-1}^{(\epsilon_{n-1,n})})\cdots(R_{1,n+1}^{(\epsilon_{1,1})}\cdots R_{n,n+1}^{(\epsilon_{1,n})}).$$

Transitivity conjecture. The element $\mathbf R^{(\boldsymbol{\epsilon})}$ solves the QYBE. This is expected to provide a large noncommutative class of QYBE solutions analogous to the classical transitivity construction; the supplied context does not state whether it has been resolved.