Reconstructible

Reconstructible is an adjective used to describe something that can be restored to its original form, state, or content from incomplete, corrupted, or partial information. The concept appears across disciplines, often with the implication that restoration is possible under certain assumptions, measurements, or constraints. In information theory and data processing, a signal or dataset is reconstructible if it can be recovered accurately from observed data, given a known encoding, redundancy, or error-correcting scheme. In fields such as archaeology, forensics, and paleontology, reconstruction refers to building a plausible interpretation or model of a scene, artifact, or sequence from fragmentary evidence.

In graph theory, reconstructibility has a precise technical meaning. A graph is reconstructible if it is uniquely determined up to isomorphism by its deck—the multiset of all vertex-deleted subgraphs. The Reconstruction Conjecture, proposed by Kelly and Ulam in 1942, asserts that every graph with at least three vertices is reconstructible, though the conjecture remains unproven. Researchers have verified reconstructibility for many classes of graphs and for extensive computational ranges, but a general proof has not been found.

Limitations of reconstructibility arise from incomplete data, measurement error, or intrinsic symmetries that obscure distinctions between objects. In some contexts, reconstruction is only possible under specific models, constraints, or noise levels; in others, information loss or ambiguous equivalence classes makes unique restoration impossible.

Overall, reconstructibility signals the potential for faithful restoration, with the understanding that success depends on the information available and the framework used to interpret it.