AbstractThis work introduces a unified theoretical framework for the classification, prediction, and structural interpretation of matter based on geometric stability principles. Insteadof treating chemical elements as entries in a discrete periodic table, we formalize matteras a continuous set of admissible configurations in a high-dimensional state spacedefined by nuclear composition, quantum structure, and temporal persistence. A generalized stability functional is constructed by combining binding energy, Coulombinteraction, shell effects, deformation contributions, and decay channels into a singlevariational structure. Within this framework, a chemical element is rigorously definedas a local minimum of the instability functional under admissibility constraints. Thisreplaces enumeration-based classification with a geometric criterion of existence. We demonstrate that the conventional periodic table emerges as a low-dimensionalprojection of a higher-dimensional stability manifold. Unknown elements are thereforereinterpreted not as successive atomic numbers, but as previously unresolved localminima in the stability landscape of matter. This leads to a predictive formulation inwhich candidate nuclei are identified through optimization in ( (Z, N) ) -space. A numerical stability map is constructed for the superheavy region, revealing a primarybasin of enhanced stability centered near (Z 114–120) and (N 184), consistent with shell-closure effects and reduced fission probability. A secondary, shallower basin is identified for (Z 126–134) and (N 190–200), corresponding to short-lived but structurally coherent configurations. Beyond this region, instability increases rapidly due to Coulomb repulsion andspontaneous fission, defining a natural boundary for atomic existence. The framework further establishes a classification hierarchy of matter states — stable, metastable, boundary, and forbidden — based on the topology of the stabilityfunctional. This enables a predictive atlas of nuclear configurations, including explicitisotope candidates, decay regimes, and experimental targeting strategies. Conceptually, the work introduces informational chemistry as a new layer of physicaldescription in which matter is characterized not only by its energy but also by itsstructural organization and persistence. In this view, chemical elements are notprimitive entities but emergent solutions of a constrained stability problem.
Roman Lukin (Mon,) studied this question.