General $B(m,n)$ triviality conjecture for inhomogeneous deformations

Let $B(m,n)=\mathfrak{osp}(2m+1|2n)$ with $m+n\geq 2$, and let $\mathrm{gb}$ denote the collection of deformation parameters in the $\gamma$-deformation. General $B(m,n)$ conjecture. The $\gamma$-deformation of $B(m,n)$ is trivial if and only if

$$\mathrm{gb}=0.$$

The surrounding results prove the corresponding statement for $B(0,n)$ when $n\geq 2$; the claim extends this triviality criterion to all $B(m,n)$ with $m+n\geq 2$.