Resolving the Hubble Tension as a Scale-Dependent Projection Effect in the Supra-Omega Resonance Framework (SORT)

The current \( 5\sigma \) discrepancy between the CMB–inferred value of the Hubble parameter \( H_{0}^{\mathrm{CMB}} \)and local measurements \( H_{0}^{\mathrm{local}} \) represents one of the most persistent tensions in modern cosmology. A key element highlighted in the Special Issue Call is the emerging correlation between the inferred value of \( H_{0} \)and the redshift of the source. In this work we examine the possibility that this correlation originates not from new dynamical physics but from scale-dependent projection effects within the Supra-Omega Resonance Theory (SORT), a mathematically formulated, non-dynamical operator framework. SORT introduces two complementary projection sectors, \( \Pi_{\mathrm{early}} \) acting predominantly on long-wavelength modes (\( k \rightarrow 0 \)) and \( \Pi_{\mathrm{late}} \) acting on short-wavelength modes, encoded through a resonance kernel \( \kappa(k) \). The resulting Hubble drift arises from a weighted spectral integral of the amplification function \( \eta(k) = \kappa(k)-1 \), \( \delta_H \propto \int \eta(k)\, W_H(k)\, \mathrm{d}k \), where \( W_H(k) \) is the expansion-weighting window associated with distance–redshift estimators. Using the fully reproducible MOCK,v3 numerical framework, SORT yields a scale-dependent structural drift of \( \delta H/H_0 = 0.0800 \), close to the observed \( \delta H/H_0 = 0.0831 \), without introducing new fields, modifying general relativity, or invoking early dark energy. These results suggest that the Hubble tension may arise from k-dependent projections of one and the same underlying structural state, rather than from inconsistencies in late- or early-universe physics.