approach to BRST formalism \[4-15\]. First of all, we focus on the derivation of the above symmetries in the context of 1$D$ rigid rotor. In this connection, we note that the gauge-fixing term (${\dot\lambda}-p_{r}$) remains invariant under $s_{(a)d}$. Furthermore, we observe that this term has its geometrical origin in the co-exterior derivative ($\delta$) because $\delta \lambda^{(1)}\,=\,\ast \,d \ast (dt \lambda(t)) \equiv {\dot \lambda(t)}$ where $(\ast )$ is the Hodge duality operation on the 1$D$ manifold. Here we have taken the 1-form as: $\lambda^{(1)}=dt\lambda(t)$. According to the basic tenets of AVSF, the invariance of the gauge-fixing term implies that this quantity should remain independent of the “soul" coordinates ($\theta, \bar\theta$) when we generalize it onto the (1, 2)-dimensional supermanifold parameterized by the superspace coordinates ($t, \theta, \bar\theta$) where the pair ($\theta, \bar\theta$) is a set of Grassmannian variables (with ${\theta}^2 =  {\bar\theta}^2 = 0,\,
\theta\bar\theta + \bar\theta\theta = 0$). In older literature \[28\], the latter coordinates have been christened as the “soul" coordinates and $t$ has been called as the body coordinate. In other words, we have the following equality $$\begin{aligned}
\star \,{\tilde d} \star   \tilde \lambda^{(1)}(t,\theta, \bar{\theta})\,-\,P_{r}(t,\theta,\bar{\theta})\,=\,
\ast  \,d \ast  \lambda^{(1)}(t)\,-\,p_{r}(t),\end{aligned}$$ where $\star  $ is the Hodge duality operation on 