Axiomatic Necessity and Impedance-Based Cosmology

The Theory of Axiomatic Necessity (TNA) proves that cosmological redshift is a consequence of structural attenuation within an impedance-based medium, not metric expansion. By applying a generalized Heaviside balance condition, this framework accounts for signal energy loss while preserving the image sharpness and spectral coherence observed in high-redshift deep fields. Standard cosmology attempts to maintain ontological closure within the observable domain ($\mathcal{N}_0$), necessitating the introduction of dark energy and inflation as auxiliary patches. This paper reformulates the universe as an Axiomatic Plenum characterized by a finite propagation impedance $(\sim377\,\Omega)$, where redshift arises from deterministic structural dissipation rather than recessional velocity. This reinterpretation eliminates the requirement for dark energy, reclassifies expansion as a projection artifact, and provides falsifiable predictions regarding cosmological time dilation and surface brightness scaling. The result is a steady-state, non-expanding universe governed by axiomatic structural constraints and the principle of structural honesty.