Commutation conjecture for the four-point DT operator and the normalized R-matrix

Let $\mathsf{F}$ be the Fock space, let $\mathsf{RR}^{H}_{\mathsf{F},\mathsf{F}\otimes\mathsf{F}}$ denote the four-point operator in cohomological DT theory, and let $\widetilde{\mathsf{R}}$ be a normalization of the R-matrix satisfying $\widetilde{\mathsf{R}}\propto\mathsf{R}_{\mathsf{F},\mathsf{F}}(1)\in\operatorname{End}(\mathsf{F}\otimes\mathsf{F})$. Commutation conjecture. The operators commute:

$$\mathsf{RR}^{H}_{\mathsf{F},\mathsf{F}\otimes\mathsf{F}}\widetilde{\mathsf{R}}^{(23)}=\widetilde{\mathsf{R}}^{(23)}\mathsf{RR}^{H}_{\mathsf{F},\mathsf{F}\otimes\mathsf{F}}.$$

This is presented as the analogue of the RTT relation for the four-point operator. The supplied passage gives no resolution or further evidence for this cohomological statement.