Generic isolation conjecture for Hodge classes on high-dimensional hypersurfaces

Let $V$ be the parameter space of smooth hypersurfaces of degree $d\geq 2\frac{{\sf m}+2}{{\sf m}-2}$ in $\mathbb{P}^{{\sf m}+1}$, with ${\sf m}\geq 4$. A Hodge class of $Y_t$ is called isolated when every component of the Hodge locus in the relevant open set is an orbit of $\operatorname{PGL}({\sf m}+2,\mathbb{C})$ acting on $V$. Generic isolation conjecture. There is a Zariski open subset $U\subset V$ such that the Hodge classes of every $Y_t$ with $t\in U$ are isolated; equivalently, all components of the Hodge locus in $U$ are the orbits of $\operatorname{PGL}({\sf m}+2,\mathbb{C})$ acting on $V$. This is presented as a stronger statement than the preceding maximal-rank conjecture and is not resolved in the source.