A Proof of the Graph Reconstruction Conjecture via Ordered Vertex Feature Sequences

We prove the Graph Reconstruction Conjecture (Kelly, 1957; Ulam, 1960), which asserts that every finite simple graph on n 3 vertices is uniquely determined, up to isomorphism, by its multiset of one-vertex-deleted subgraphs (the deck). Building upon the ordered vertex pattern framework established in our earlier work (Wang, 2026), we introduce an upgraded feature extraction rule: for every permutation of the vertices, we record, for each vertex, its adjacency relations to all vertices in that permutation (including itself), yielding a set of binary feature sequences. We show that the (n-1) -th layer of this upgraded invariant is fully determined by the deck. By analyzing the intersection structure of the feature sequence multisets arising from distinct cards, we uniquely recover, for each vertex, the entire collection of its feature sequences across all (n-1) -tuples. Once vertex identities are recovered, all edges are directly read off from the sequences. The proof is constructive, makes no appeal to the symmetry of the graph, and provides a complete resolution of the conjecture.