The generalized edge reconstruction conjecture

Let $n\geq 4$, and let $G_1,\dots,G_k$ be a collection of $n$-edged graphs for some $k\geq 1$. Write $\coprod_{i=1}^k\operatorname{ED}(G_i)$ for the disjoint union of their edge decks. Generalized edge reconstruction conjecture. For every $k\geq 1$, the collection $\{G_1,\dots,G_k\}$ is uniquely reconstructible from $\coprod_{i=1}^k\operatorname{ED}(G_i)$. This is explicitly disproved in the paper: for every $n\geq 2$, some finite collection is not reconstructible, so the conjecture is false.