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/zb) + γ₀·ln (1+z) ²·e^ (-z/zₕ) 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 (H₀ₗocal = 73. 05 from H₀cosmo = 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