Monotonicity of the nilpotency index under DS reduction

Let ${\cal V}$ be a VOA corresponding to a four-dimensional ${\cal N}=2$ SCFT, and let DS reduction produce another VOA corresponding to a four-dimensional ${\cal N}=2$ SCFT. Denote the stress-tensor nilpotency index before and after reduction by $\mathfrak{n}_{\rm UV}$ and $\mathfrak{n}_{\rm IR}$, respectively. DS-reduction monotonicity conjecture. The nilpotency index does not increase under DS reduction.

$$\mathfrak{n}_{\rm IR}\leq\mathfrak{n}_{\rm UV}.$$

This is the VOA formulation of the proposed RG monotonicity under Higgsing, where Higgsing is implemented by DS reduction. The source gives no general proof.