Entropic Future–Mass Projection Gravity and the Cosmic Radio–Dipole Excess: From Covariant Kernels to Quantitative Ultra–Large–Scale Clustering

Multiple wide–area radio surveys report a source–count dipole whose amplitude exceeds the purely kinematic expectation inferred from the CMB dipole by a factor of ∼ 3–4, while remaining aligned with the CMB dipole direction. This tension, now detected at ≳ 5σ when combining NVSS, RACS–low and LoTSS–DR2, challenges the vanilla ΛCDM picture in which the radio dipole is dominated by Doppler and aberration effects with only a small clustering contribution. In this paper we present a quantitative implementation of Future–Mass Projection (FMP) gravity as a potential explanation of this anomaly. FMP is a diffeomorphism–invariant, bilocal, time–nonlocal extension of GR in which the effective source is a causal projection of the baryonic energy–momentum tensor along a finite, advanced horizon on a closed time path. On cosmological scales the theory can be parametrised by a scale– and time–dependent modification of the Poisson equation, μ(a, k), and lensing response, G(a, k), that are determined by the Fourier transform of the covariant kernel. We make three key advances compared to previous work. First, we provide an explicit mapping from an “entropic” Newtonian kernel, defined as the Hessian of a coarse–grained entropy functional in the space of disc and large–scale density configurations, to the cosmological response functions μ(a, k) and G(a, k). This leads naturally to a two–lobe scale dependence, with μ(a, k) < 1 on quasi–linear scales k ∼ 0.02–0.2 hMpc−1 and μ(a, k) > 1 on ultra–large scales k ≲ 0.01 hMpc−1, thereby reconciling a modest 10–15% suppression of fσ8 with an ultra–large–scale growth boost. Second, we fix the kernel parameters (ΔT, η, k1, k0) using two independent data sets: low–redshift redshift–space distortion measurements of fσ8 and galaxy rotation curves. This yields a single family of CTP kernels that already satisfies Solar–System, PPN and GW– speed constraints, and mildly alleviates the S8 tension. Third, using these pre–determined kernels, we compute the ultra–large–scale clustering boost factor BULS that enters the radio source–count dipole. We model the selection function W(z) and linear bias b(z) for NVSS, RACS–low and LoTSS–DR2, and evaluate the relevant integrals for BULS(ΔT, η, k0), propagating uncertainties from the kernel parameters and the source populations. For the kernel that best fits fσ8 and rotation curves we obtain a blind prediction RFMP ≡ dobs/ dkin = 3.2 ± 0.4, to be compared with the combined radio–dipole measurement Robs = 3.67 ± 0.49. A simple χ2 comparison shows that the anomaly is naturally reproduced within FMP without invoking particle dark matter, while remaining consistent with current large–scale structure and background probes. We discuss degeneracies, parameter–space constraints and the status of competing explanations for the radio–dipole excess.