Chemical Hyperstructures, SuperHyperstructures, and SHv-Structures: Toward a Generalized Framework for Hierarchical Chemical Modeling

The concept of aClassical Structure provides a broad mathematical framework, whereas a Hyperstructure arises via the powerset construction, and an 𝑛-Superhyperstructure is obtained by iterating this construction n times [1]. Intuitively, the n-th powerset corresponds to 𝑛 successive applications of the powerset operator. Below, we recall the fundamental definitions and illustrate them with elementary examples. In the chemical sciences, various hyperstructural frameworks—such as Chemical Hyperstructures—have also been studied. In this paper, we introduce the notion of a Chemical Superhyperstructure and examine its foundational properties. We further extend the idea of a Weak Chemical Hyperstructure by defining the Weak Chemical Superhyperstructure via the Weak Superhyperstructure (SHv-Structure) framework, and provide an overview of its behavior. These constructions offer a concise and flexible means to represent hierarchical relationships in chemical systems.