Geometric Reinterpretation of Cosmological Redshift in a Non-Expanding Higher-Dimensional Framework: Modified Luminosity Distance, Effective Timescale, and Sovereign Empirical Verification Pathways

This paper presents a geometric reinterpretation of cosmological redshift within the Unified Dimensional Cohesion Theory (UDCT). Building upon the bidirectional projection operator ΨBD and the higher-dimensional screening correction ∆geo(z, ξ0) developed in previous works, we demonstrate that the observed redshift–distance relation can be understood as arising from cumulative photon-momentum leakage into higher-dimensional degrees of freedom, rather than from physical spacetime expansion. The Hubble constant is reinterpreted as an intrinsic geometric relaxation timescale, yielding explicit operational formulas for luminosity distance and effective lookback time. These expressions remain consistent with galactic dynamics and alleviate the Hubble tension without invoking dark energy. We argue that legacy cosmological observables processed under FLRW assumptions create methodological challenges when testing non-expanding frameworks. Accordingly, we outline sovereign empirical verification pathways and propose a concrete roadmap for rigorous tests of the redshift reinterpretation, with emphasis on independent forward generative simulations for the cosmic microwave background and other key observables. Future work will also explore extensions toward neutrinos and fermionic sectors within the cross-scale unification framework.