Topological Horizon Lensing: γCDM Correction to Cosmological Distances

We present the results of a systematic forensic investigation into the Hubble Tension. Starting from the 4–6σ discrepancy between local (H₀ ≈ 73) and CMB (H₀ ≈ 67.4) measurements, we follow a strictly data-driven path through three generations of models: (i) a linear logarithmic correction γ · ln(1+z), which provided the first signal (ΔBIC = −6.2);(ii) a quadratic form γ₀ · [ln(1+z)]², which exploded in significance (ΔBIC ≈ −739) but predicted an unphysical CMB;(iii) the final two-component LOG²-Decay model: Δμ(z) = A·e^(-z/z_b) + γ₀·[ln(1+z)]²·e^(-z/z_h) which achieves ΔBIC ≈ −760 against ΛCDM using 4,010 cosmological probes (Pantheon+ SNe Ia, Quasars, Cosmic Chronometers), provides a phenomenological route to alleviating the Hubble Tension (H₀_local = 73.05 from H₀_cosmo = 67.4), and remains compatible with the CMB at the level of background-distance extrapolation. The logarithmic component can be mapped, under the Möbius–Kerr hypothesis, to an effective Container Black Hole spin parameter of a/M ≈ 0.72. Endorsement: astro-ph.CO - physics.data-an - stat.AP