The principal-curvature conjecture for Fourier dimension of hypersurfaces

A hypersurface $M$ in Euclidean space has principal curvatures, the eigenvalues of its Weingarten map, at each point. Its Fourier dimension, denoted by $\dim_F(M)$, measures the strongest decay of Fourier transforms of finite measures supported on $M$. Let $M$ be a $d$-dimensional orientable hypersurface in $\mathbb{R}^{d+1}$. Suppose $k$ of the $d$ principal curvatures are nonvanishing, and the other $d-k$ principal curvatures are always zero. Principal-curvature conjecture. Then

$$\dim_F(M)=k.$$

The claim would relate Fourier dimension directly to the number of nonzero principal curvatures, extending the known cases of hyperplanes and hypersurfaces with nonvanishing Gaussian curvature. The supplied text does not state whether this conjecture has been resolved.