The Algebra in Natural Structures

Francesco Peña-Garcia; John Medina-Diaz · Zenodo (CERN European Organization for Nuclear Research) (2026) · DOI: 10.5281/zenodo.19490730

Resumen

Natural structures are assembled with the formation of NE-connections which are a generalization of attraction forces. Here, we construct two nested axiomatic systems in which NE-connections can be understood as an algebraic operation. Then, we define a partial order $\leq$ that represents the relation ``being part of'' between the elements of the space of natural entities. We prove that the collection of elements of an arbitrary natural structure $n$ which is denoted as $X_n$ is a commutative semigroup $(X_n,\bullet)$ in which every element is idempotent. The operator $\bullet$ represents the act of NE-connecting. We follow this by proving the codefinition of $\leq $ and $\bullet$ in finite NEs as well as their compatibility. Finally, we propose a mathematical definition of the collection of families of NE-connections and point out its relationship with $X_n$.

Instituciones: Universidad Nacional Mayor de San Marcos