Manvel's bounded-deletion reconstruction conjecture for graphs

Let $\ell\in\mathbb{N}$. A graph is $\ell$-reconstructible if its isomorphism type is determined by its $(n-\ell)$-deck, the multiset of induced subgraphs obtained by deleting $\ell$ vertices from an $n$-vertex graph.

Manvel's conjecture. For each $\ell\in\mathbb{N}$, there exists a threshold $M_\ell$ such that every graph with at least $M_\ell$ vertices is $\ell$-reconstructible.

This extends the classical Reconstruction Conjecture to deletion of an arbitrary fixed number of vertices. The source does not give a resolution of this conjecture.