On the triviality of inhomogeneous deformations of $\mathfrak{o}\mathfrak{s}\mathfrak{p}(1\mathrm{\mid }2n)$

We analyze the triviality of inhomogeneous $\gamma$-deformations of the oscillator Lie superalgebra $B(0,n)=\mathfrak{o}\mathfrak{s}\mathfrak{p}(1\mathrm{\mid }2n)$. As the main theorem, we show that for $n\ge 2$, the $\gamma$-deformation is trivial if and only if all deformation parameters vanish. The proof is based on the explicit construction of $2n$ certificates (left null space vectors $c$ satisfying $c^{\mathrm{\top }}{A}_{\mu }=0$ and $c^{\mathrm{\top }}{L}_{\mu }\mathrm{\ne }0$) for the structure constant matrices $A_{\mu }$ of the coboundary operator. We provide a unified construction of certificates classified into three Families, and in particular clarify the geometric meaning of the coefficient $1+{\delta }_{n,2}$ that appears in the Family~III certificate. We also discuss the contrast with the exceptional case of $B(0,1)=\mathfrak{o}\mathfrak{s}\mathfrak{p}(1\mathrm{\mid }2)$ (where all deformations are trivial). As an appendix, we outline the computational verification performed using exact rational arithmetic over $\mathbb{Q}$.