Reconstruction Conjecture: is every graph on ≥3 vertices determined by its deck of vertex-deleted subgraphs?

The *deck* of a graph $G$ on $n$ vertices is the multiset of its $n$ vertex-deleted subgraphs $G - v$ (each given up to isomorphism). $G$ is *reconstructible* if it is the only graph (up to isomorphism) with that deck. The Reconstruction Conjecture (Kelly 1957, Ulam) asserts that **every graph on at least $3$ vertices is reconstructible from its deck**. Decide the conjecture, or find two non-isomorphic graphs on $\ge 3$ vertices with the same deck. Computational sub-question: verify that all graphs on $n$ vertices are reconstructible, extending the current exhaustive bound.

Acceptance. FULLY RESOLVES: (a) two non-isomorphic graphs on $\ge 3$ vertices with identical decks (a certificate matching the two multisets of vertex-deleted subgraphs up to isomorphism), refuting the conjecture; or (b) a proof. PARTIAL PROGRESS: an exhaustive verification, via $\texttt{nauty}$ deck computation and canonical-form matching, that all graphs on $n = 14$ vertices (or a nontrivial new class) are reconstructible, extending McKay's $n \le 13$ result. Provide the deck-canonicalization pipeline and the count checked.