Cosmic Radio Dipoles, Fractal Variance, and Prime-Indexed Information Geometry: A Universal Model Framework Analysis with LoTSS-DR3 and NVSS.

Cosmic radio surveys provide a uniquely sensitive probe of large‑scale anisotropy and matter distribution. Using the LOFAR Two‑metre Sky Survey Data Release 3 (LoTSS‑DR3) and the NRAO VLA Sky Survey (NVSS), we perform a unified analysis of five radio‑cosmology diagnostics designed to test the Universal Model Framework (UMF), an information‑theoretic approach in which large‑scale structure emerges from a prime‑indexed fractal geometry. The expanded depth and sky coverage of LoTSS‑DR3 enable the first variance‑scaling measurements down to ≃3.4′, while NVSS provides complementary all‑sky constraints at 1.4 GHz.We find that the combined LoTSS‑DR3 + NVSS number‑count dipole remains a factor of 5–7 above the standard kinematic expectation, with no detectable frequency dependence across 144–1400 MHz. Monte‑Carlo–corrected quadrupole‑to‑dipole ratios converge to C₂/C₁ ≃ 0.2–0.3, consistent with both ΛCDM and the UMF prediction once mask‑induced suppression is accounted for. Variance‑scaling measurements do not yet reach the prime‑fractal regime, and prime‑multipole tests yield null results at current sensitivity. The radio–lensing cross‑correlation is fully consistent with ΛCDM expectations.Taken together, these results show that the radio dipole excess is robust across frequency and survey methodology, while higher‑order UMF signatures remain below current detection thresholds. We outline a path toward decisive tests using deeper flux thresholds, full‑sky low‑frequency surveys, and injection–recovery simulations. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.