Inhomogeneous transfer-matrix eigenvalue conjecture for the open eight-vertex model

Let $L\geqslant 1$, let $u_1,\dots,u_L$ be inhomogeneity parameters, and define the inhomogeneous open-boundary transfer matrix

$$\mathcal T(u|u_1,\dots,u_L)=\operatorname{tr}_0\left(K_0^+(u)U_{0,[1,L]}(u|u_1,\dots,u_L)K_0^-(u)\bar U_{0,[1,L]}(u|u_1,\dots,u_L)\right),$$

where $K^-(u)=K(u)$, $K^+(u)=K(u+2\eta)$,

$$U_{0,[1,L]}(u|u_1,\dots,u_L)=R_{0L}(u+u_L)\cdots R_{01}(u+u_1),$$ $$\bar U_{0,[1,L]}(u|u_1,\dots,u_L)=R_{01}(u-u_1)\cdots R_{0L}(u-u_L).$$

Set $\eta=\pi/3$, and let $K(u)$ be the $K$-matrix specified by the coefficients in the source, evaluated at $t=\pi/6$. Inhomogeneous eigenvalue conjecture. The transfer matrix possesses the eigenvalue

$$\Lambda_L=\operatorname{tr}(K^+(u)K^-(u))\prod_{j=1}^L\left(a(u+u_j)+b(u+u_j)\right)\left(a(u-u_j)+b(u-u_j)\right).$$

This conjecture extends the explicitly computed homogeneous transfer-matrix eigenvalue to the inhomogeneous open eight-vertex model. The supplied text does not state whether it has been proved or disproved.