A Single Effective Framework Underlying Galaxy Rotation Curves and the Hubble Tension

We investigate whether two long-standing observational anomalies—flat galaxy rotation curves and the Hubble constant tension—may originate from a common effective mechanism operating in low-density environments. We introduce a minimal phenomenological framework in which departures from Newtonian expectations arise from a bounded saturation of the effective gravitational response at the level of kinematic inference, without invoking dark matter particles or modifying the background Friedmann expansion or early-universe physics. In the galactic regime, the empirically established low-acceleration phenomenology arises as the saturated limit of the effective kinematic inference, with no modification of the gravitational law. Applied to disk galaxies, the framework reproduces the main features of observed rotation curves across a broad range of morphologies using baryonic matter alone, with stable parameter values and no halo-by-halo tuning; comparisons with representative galaxies from the SPARC sample show that the effective saturation scale correlates with observed surface-density-dependent trends. At cosmological scales, the same bounded-response structure predicts environment-dependent shifts in the locally inferred expansion rate: for typical void density contrasts the deep-saturation regime applies, yielding a fractional shift $\Delta H/H \simeq \delta_\rho f_{\max}$ without additional cosmological degrees of freedom or any change to the global expansion history. We examine robustness, degeneracies, and limitations, and outline distinctive observational signatures, including environment-dependent redshift drift and weak-lensing modifications in extreme low-acceleration regimes. We finally isolate a structural expansion sector: under an explicitly stated rank–time dictionary hypothesis, the accelerated component of expansion is carried by the branching of projectively distinguishable histories—an exact Pell count with rate $\log(1+\sqrt{2})$—rather than by a dark-energy fluid, the naive state-volume reading is quantitatively excluded, and the asymptotic de Sitter limit is upgraded from a free late-time fit to a calibrated spectral steady state, with no numerical prediction of $H_\infty$. Interpretive reading (interpretation, not a derived result): the late-time anomalies trace inference bounds rather than new substances, and accelerated expansion is a property of the projective record.