Modified reconstruction conjecture for trees beyond the known exceptions

For an $n$-vertex tree, its $(n-\ell)$-deck is the multiset of induced subgraphs obtained by deleting $\ell$ vertices. A tree is $\ell$-reconstructible if it is determined up to isomorphism by its $(n-\ell)$-deck.

Modified tree reconstruction conjecture. For $n\ge 2\ell+1$, except when $(n,\ell)\in\{(5,2),(13,6)\}$, every $n$-vertex tree is $\ell$-reconstructible. The threshold on $n$ is known to be sharp.

This modifies Nýdl's conjecture by excluding the known five-vertex and thirteen-vertex exceptions. The source presents the statement as a conjectural modification; the supplied parser gives no evidence that it has been resolved.