The two-actions conjecture for degenerate projective hypersurfaces

Let $X\subseteq\mathbb{P}^{n+1}$ be a degenerate hypersurface admitting an induced additive action, where an induced additive action is an additive action obtained from the ambient projective action. Two-actions conjecture. There are at least two induced additive actions on $X$ up to equivalence. This would complement the cited result for projective hypersurfaces; the conjecture is presented as an open question in the paper.