Independence of affine fusion products from evaluation parameters

Let $\g$ be an affine Kac–Moody algebra, and let $V_1,\ldots,V_n$ be integrable representations with cyclic vectors. For pairwise distinct complex numbers $Z=(z_1,\ldots,z_n)$, form the evaluation representations $V_i(z_i)$ and their fusion product

$$V_1(z_1)*\cdots*V_n(z_n).$$

Fusion-product independence conjecture. The corresponding fusion product does not depend on $Z$ as a representation of $\g\otimes\mathbb{C}[u]$.

Parameter independence would make the fusion product an intrinsic construction for these affine Kac–Moody representations rather than one depending on the chosen evaluation points. The supplied text does not state whether this claim is proved or remains open.