TSO: Time Space Oscillation-Spin and Pauli-Spin: A Direct Comparison

TSO: Time Space Oscillation-Spin and Pauli-Spin: A Direct Comparison This work provides the long-awaited direct comparison between the spin structure of Time--Space Oscillations (TSO) and the established spinorial formalisms of Pauli, Weyl, and Dirac. Earlier TSO publications identified a spin-like structure within the cyclic Time--Space representation, but its precise relation to conventional fermionic spin had not yet been established algebraically. Starting from the TSO cyclic variable and its reciprocal self-referencing structure, the present analysis derives the four compatible phase sectors and their normalization, yielding a normalized two-component TSO representation. Its quarter-cycle transformations are then expressed directly through the Pauli matrices and satisfy the characteristic relations Q^2=-I andQ^4=I. The continuous TSO representation is subsequently connected to physical spin direction through the standard Pauli bilinears. The resulting correspondence is stronger than a formal analogy. The TSO cyclic spin degree of freedom and the conventional Pauli spin describe the same physical fermionic spin degree of freedom, while TSO and Pauli provide different representations of that structure. The comparison further places the two-component TSO representation in direct relation to the Weyl sectors and the four-component Dirac formalism. The paper therefore closes an important open step in the TSO research program: it establishes explicitly how the spinorial structure generated by the TSO cyclic representation corresponds to the established Pauli--Weyl--Dirac description of fermionic spin. For refence of TSO as a conceptual QM equivalent please read. Time–Space Oscillations: A Geometric and Deterministic Approach to Relativistic and Quantum PhenomenaZenodo DOI: 10.5281/zenodo.17534734The foundational article introducing the TSO framework and its applications to both relativistic and quantum phenomena. Time Dilation and the Nature of Gravitational and Inertial ForcesZenodo DOI: 10.5281/zenodo.17543059Explores the TSO perspective on time dilation and the interplay of inertial and gravitational forces. Time–Space Oscillations and ElectromagneticsZenodo DOI: 10.5281/zenodo.17591325Applies the TSO model to electromagnetic phenomena, revealing novel interpretations of wave propagation and field interactions. Time–Space Oscillations and Quantum Mechanics Zenodo DOI: 10.5281/zenodo.17670668Extends TSO to encompass quantum mechanical principles, including Heisenberg uncertainty, Schrödinger dynamics, path integrals, entanglement, zero-point energy, and the Quantum Zeno effect. For an overview of related work and publications, visit:https://ndl1971.github.io/time-space-oscillations/