Non-self-similarity conjecture for a Lie superalgebra and its analogue

Let $\mathbf R=\operatorname{Lie}(v_0,v_1)$ be the Lie superalgebra whose generators $v_0,v_1$ are defined by the pivot construction referenced in the source. A Lie superalgebra $\mathbf R$ is self-similar if it admits a self-similarity embedding of the type considered in the paper. Non-self-similarity conjecture. The Lie superalgebra $\mathbf R$ is not self-similar; likewise, the Lie superalgebra of the cited fractional-partial-derivative example should not be self-similar. The first assertion is presented together with the cited example, while the analogous assertion for the other Lie superalgebra remains conjectural.