Levitina–Sukochev–Zanin's interpolation characterization for symmetric sequence spaces

Let $E$ be a quasi-Banach symmetric sequence space. For functions or sequences $f$ and $g$ with nonincreasing rearrangements $f^*$ and $g^*$, write $f\triangleright g$ when

$$\forall t>0,\quad \int_t^\infty f^*\geq\int_t^\infty g^*.$$

The space $E$ is right-$2$-monotone if there exists $C>0$ such that, for all $f\in E$ and $g\in L_0$, $|f|^2\triangleright|g|^2$ implies $g\in E$ and $\lVert g\rVert_E\leq C\lVert f\rVert_E$. Levitina–Sukochev–Zanin's conjecture. $E$ is right-$2$-monotone if and only if there exists $p\in(0,2]$ such that $E$ is an interpolation space between $\ell^p$ and $\ell^2$. This conjectured characterization links right-majorization monotonicity with interpolation of the classical sequence spaces $\ell^p$ and $\ell^2$; the supplied source does not indicate whether it has been resolved.