The Dynamical Fourier Field Resolution of the Hubble Tension: Coherence Decay, Residual Spectral Force, and the Elimination of Dark Matter

This manuscript provides a first-principles resolution to the 7.1\sigma Hubble Tension. Utilizing the Dynamical Fourier Field (DFF) framework established in Papers I–IV, we demonstrate that the discrepancy between local distance-ladder measurements (\Hlocal \approx 73.5) and CMB-inferred values (\HCMB \approx 67.2) is not a measurement error or a sign of "Early Dark Energy," but a structural necessity of spectral coherence evolution. Key Breakthroughs: The Second Law of DFF: We derive how the Hubble parameter is a projection of the global spectral coherence decay rate (d\Cg/ds). Because coherence decays monotonically, \Hlocal > \HCMB is an inescapable prediction of the framework. Elimination of Dark Matter: We introduce the Residual Spectral Force (RSF). The RSF is a long-range coherence coupling between baryonic structures that accounts for galactic rotation curves and the Bullet Cluster lensing offset, rendering CDM particles unnecessary. Dynamical Dark Energy: We show that "Dark Energy" is the emergent tension of the spectral metric relaxing toward maximum dispersion, yielding an effective equation of state w_{\mathrm{eff}} \approx -0.988. The Projection Kernel: We provide an explicit, redshift-dependent transition model based on a Gaussian spectral integral that matches the 7.1\sigma tension with no fine-tuning. The numerical prediction and observational tests of this paper can be found in part 2 at https://doi.org/10.5281/zenodo.19615676