Manvel's eventual reconstructibility conjecture for graphs

For $l\in\mathbb{N}$, let an $l$-deck be the multiset of $l$-vertex induced subgraphs of a graph, and call a graph $\ell$-reconstructible if it is determined by its $(n-\ell)$-deck. Manvel's conjecture. For $l\in\mathbb{N}$, 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 from vertex-deleted decks; the paper states that no proof was known for any fixed $\ell$, while the present work studies threshold bounds for special graph classes.