We present the results of a systematic forensic investigation into the Hubble Tension. Starting from the discrepancy between local (H₀ ≈ 73) and CMB (H₀ ≈ 67. 4) measurements, we follow a data-driven path through three generations of luminosity-distance corrections: (i) a linear logarithmic correction γ·ln (1 + z), which provided the first signal; (ii) a quadratic form γ₀·ln (1 + z) ², which emerged as the most parsimonious empirical deformation; and (iii) the final two-component LOG²-Decay candidate model: Δμ (z) = A·e^ (-z/zb) + γ₀·ln (1 + z) ²·e^ (-z/zₕ) In the current canonical run, using 1, 580 Pantheon+ SNe Ia with STAT+SYS covariance, 2, 036 quasars (z > 0. 7 plus 13 retained local group-7 calibration objects), 30 Cosmic Chronometers, and a Planck shift-parameter prior, the LOG²-Decay model improves over ΛCDM by ΔAIC = −54. 1 and ΔBIC = −29. 3 under a fixed CMB anchor (H₀ = 67. 4). The best-fit correction yields A = −0. 208, zb = 1. 025, γ₀ = −0. 398, zₕ = 121. 0, implying H₀ (local) = 74. 03 km s⁻¹ Mpc⁻¹. MCMC and nested-sampling validation recover Ωc h² ≃ 0. 120 and give a nested-sampling Bayes factor ln B = 23. 76 for the likelihood used here. A DESI DR1 BAO null test, not included in the fit, gives χ²BAO / 12 = 1. 97 and rd = 145. 86 Mpc for the LOG²-Decay best fit. Predictive diagnostics also favor the model: PSIS-LOO and WAIC improve the deviance by about 42 relative to ΛCDM, with the only Pareto-k > 0. 7 warning arising from the single compressed CMB summary point rather than from the SNe, QSO, or CC data. In Block II, we present the tentative theoretical foundation for this empirical signal. By evaluating the Raychaudhuri expansion scalar in an inverted Möbius-Kerr spacetime, we illustrate how a reduced inverse-Raychaudhuri construction can reproduce the empirical correction as the integrated imprint of an effective optical shear in an inverted Möbius-Kerr geometry.
Jose Bautista (Mon,) studied this question.