This paper develops a quantitative theory for the graph reconstruction problem. From the vertex-deleted deck of an n-vertex graph, a multiset of binary row fragments is extracted and treated as formal strings to be assembled by maximum overlaps. A reconstruction is represented by a saturated symmetric assembly of these fragments into n global rows. The first part builds a finite obstruction calculus on a packet-level covering space, where overlap choices form a finite assembly category and reading failures are recorded by Cech cochains. The second part turns this into a quantitative upper-bound theory: the number of nonisomorphic realizations of a graph-realizable deck is bounded by the minimum of several finite estimators, including degree-gap compression, two-card overlaps, row-assembly counts, obstruction sectors, and automorphism orbits. This gives the first explicit exponential bound on the worst-case number of reconstructions for every fixed n. A separate certificate theorem proves a conditional sharp two-bound; if finite insertion-completeness and internal two-bound certificates are supplied, then every reconstruction fiber has size at most two. The paper does not prove the required universal certificates exist, but isolates exactly the obstruction data that future work must eliminate. Keywords graph reconstruction conjecture, maximum-overlap assembly, vertex-deleted deck, covering-space obstruction, finite Cech obstruction, nonabelian overlap transition, quantitative reconstruction bounds, degree-gap compression, certificate framework
Jianming Wang (Fri,) studied this question.