Spatial Ontology and the Emergence of Electromagnetic Phenomena from the Meta-Axiom of "Strict Mutual Exclusivity of Being and Non-Being"

This paper demonstrates that the core structures of both classical electromagnetism and special relativity — Maxwell's equations and Lorentz invariance — can be derived from a single, pre-physical axiom: the strict mutual exclusivity of Being and Non-Being. Through rigorous logical and mathematical deductions, this axiom is translated into constraints that force the physical medium we call "space" to be three-dimensional, absolutely homogeneous and isotropic, incompressible, and C¹ smooth. The only permissible deformation in this medium is the pure shear transverse wave, which at the critical shear limit γcr=1 exhibits rigid amplitude-wavelength locking, with its energy determined solely by frequency. From the wave equation of this medium, Maxwell's equations and Lorentz invariance emerge directly as mathematical consequences, not external postulates. This theory provides a single ontological foundation for both electromagnetism and special relativity, without ad hoc assumptions, and is fully consistent with all existing experiments at observable levels.