Multipartite Entanglement as a Structural Defect: Topological Classification, Hypergraph Ontology, and Thermodynamics of Self-Organization

This work proposes a structural and topological framework for the description of multipartite quantum entanglement within the Theory of Structural Articulation (TSA). Entanglement is interpreted not as an abstract algebraic property of quantum states in Hilbert space, but as a manifestation of the connectivity of a single structural defect embedded in an underlying medium. The fundamental carrier of quantum structure is modeled as a hypergraph of difference connectivity, whose irreducible hyperedges encode genuine multipartite correlations. Observable entanglement is described as a projection of this hypergraph onto a connectivity graph of pairwise correlations. A topological invariant—the first Betti number of the connectivity graph—is introduced and shown to characterize redundancy of correlation pathways and robustness of multipartite quantum resources against local losses. This provides a unified topological classification of GHZ-type states, W states, and cluster states, and explains qualitative differences in their stability. Beyond static classification, the work formulates a thermodynamic mechanism for the emergence of structural complexity in open quantum systems. Dissipative relaxation of structural conflict drives spontaneous closure of connectivity loops, leading to growth of topological redundancy and formation of highly connected phases. Multipartite entanglement is thereby interpreted as an equilibrium or quasistationary phase of a dense system of structural defects, rather than as the result of fine-tuned unitary control. The results offer a structural interpretation of multipartite entanglement, linking topology, robustness, and self-organization, and suggest new perspectives on the physical origin of scalable quantum resources for quantum information processing and quantum memory.