A Perspective on the Algebra, Topology, and Logic of Electrical Networks

ABSTRACT This paper presents a unified algebraic, topological, and logical framework for electrical one‐port networks based on Šare's ‐theory. Within this formalism, networks are represented by ‐words (jorbs) over an ordered alphabet, where series and parallel composition induce an ‐topology on ‐graphs with a theta mapping that preserves one‐port equivalence. The study formalizes quasiorders, shells, and cores, showing their structural correspondence to network boundary conditions and impedance behavior. The – metric, together with the valuation morphism , provides a concise descriptor of the impedance‐degree structure. In the computational domain, the framework is extended with algorithmic procedures for generating and classifying nonisomorphic series–parallel topologies, accompanied by programmatic Cauer/Foster synthesis workflows and validation against canonical examples from Ladenheim's catalog. The resulting approach enables symbolic‐to‐topological translation of impedance functions, offering a constructive bridge between algebraic representation and electrical realization. Overall, the paper outlines a self‐consistent theoretical and computational foundation for automated network synthesis, classification, and formal verification within the emerging field of Jorbology. The framework is also positioned for future extension to multiport (MIMO) networks, where jorbs act as combinatorial indices for efficient classification prior to full matrix‐based analysis.