Ordered Vertex Pattern Multisets, Graph Isomorphism, and Deleted-Subgraph Reconstruction

We prove that the global ordered-vertex-pattern framework is exact at the top layer and reconstruction-theoretic at lower layers. For every finite graph G, the top global layer determines G up to isomorphism, and for every 1 r |V (G) |-1, the codimension-r global layer determines the full r-vertex-deleted deck. Consequently, any known r-reconstructibility theorem immediately yields a completeness theorem for the corresponding lower global layer. The paper then develops exact consequences of this bridge: lower layers determine induced-subgraph counts up to the visible order, transfer completeness to trees, 3-regular graphs, and complement classes, and extend the tree case to linear-range smaller-card consequences. Within the low-symmetry direction, the main object-level result is an unconditional bicentered multi-card reconstruction theorem on branch-distinct bicentered trees, with asymmetric distinct-leg double spiders appearing as a concrete corollary. Around this reconstruction core we record automorphism-multiplicity formulas, canonization consequences, complement transport, injective scalarizations, restricted-class completeness on complete multipartite and cluster graphs, and a compressed extension principle for directed graphs, mixed graphs, hypergraphs, and finite relational structures. The supplementary document contains only audit tables and benchmark examples; the main article is intended to stand on its theorem-level arguments and proofs.