A Dimensional Audit of Electromagnetic Unit Systems: CGS, SI/MKS, and Quantum Measurement Units

A Dimensional Audit of Electromagnetic Unit Systems: CGS, SI/MKS, and Quantum Measurement Units This paper performs a dimensional audit of the historical transition from CGS electromagnetic units to SI/MKS. While SI introduced an explicit charge dimension and redistributed dimensional structure among Coulomb's constant, vacuum permittivity, vacuum permeability, capacitance, inductance, and conductance, the resulting relationships are rarely examined as a unified dimensional system. The analysis demonstrates that Coulomb's constant, vacuum impedance, vacuum permittivity, vacuum permeability, conductance, capacitance, inductance, and the speed of light form an interconnected electromagnetic closure family. A compact closure identity, kC = c Cd \, ₀₀, is derived and shown to bind Coulomb's constant, conductance, permeability, permittivity, and wave propagation into a single dimensional structure. The paper further develops a graph interpretation of electromagnetic units and proves that the closure family forms a connected dimensional network generated by a small set of algebraically independent relationships. The Quantum Measurement Unit (QMU) framework is introduced as an alternative dimensional ontology in which these relationships are represented explicitly through ledger identities, reciprocal relationships, and closure structures. Within this framework, magnetic flux and resistance occupy distinct magnetic-charge ranks, suggesting that conventional impedance theory may compress dimensional distinctions that can be represented separately within a ledger-based unit system. The paper argues that permeability, permittivity, capacitance, inductance, conductance, and Coulomb's constant should not be viewed as isolated definitions but as members of a unified Coulomb-bound electromagnetic family. The resulting dimensional perspective provides a foundation for future work on electromagnetic closure structures, unit authority graphs, and ledger formulations of physical quantities.