Materialization and Dematerialization of Topological Defects in the Hypergraph G∗: The ZEBTS Formalism

Abstract This work develops a rigorous hyper‑topological formalism for describing the materialization and dematerialization of matter within the Law of Unity of Being and the Triune Substance (ZEBTS). Matter is interpreted not as a fundamental entity but as an emergent manifestation of the dynamics of the hyper‑topology G∗, consisting of cells of various dimensions, boundary operators, and topological measures. Material objects correspond to topological defects Dk that arise during phase transitions of the hyper‑topology, while their disappearance is associated with annihilation, stabilization, or collapse of homologies. A strict mathematical apparatus is introduced, including quantum entropy SQ, dispersion of connections Var(λk), spectral characteristics of the Laplacian Δk, and the flytron structure F=(M,∂M,I^). Conditions for the birth and disappearance of matter are obtained, stability criteria for defects are derived, and experimental tests and cosmological predictions are proposed. The work forms the basis for further development of hyper‑topological physics and integration of ZEBTS with modern theories of gravity and quantum matter.