Resolution of the Hubble Tension by a Reversible Fractal Cosmology: The Ultimate Black Hole Framework

We present a revised formulation of the Ultimate Black Hole (UBH) cosmology as a reversible and adiabatic fractal model of the Universe. In this framework, the cosmic evolution proceeds as a closed thermodynamic cycle in which the total entropy remains globally conserved, while local exchanges between fractal and non-fractal subsystems maintain adiabaticity. The Universe originates from the fragmentation of a quasi-stable UBH whose fractal horizon and inner structure imprint the initial conditions for cosmic expansion. The resulting post-burst medium inherits the information content of the UBH fractal pattern, leading to a self-similar distribution of black holes and matter with an initial spatial fractal dimension \( D_f^{\mathrm{space}}\!\simeq\!1.656 \). During cosmic evolution, \( D_f(z) \) smoothly increases toward the present-day value \( D_f(0)\!\simeq\!2 \), consistent with large-scale galaxy surveys, while the global entropy balance is preserved through the fractal factor \( F(a)=({R_c}/{\ell_c})^{H(a)} \). Fitting the UBH expansion law to the Pantheon Type Ia supernova dataset yields a statistically superior description compared to the standard \( \Lambda \)CDM model. Using a single calibrated value of \( H_0=73~\mathrm{km\,s^{-1}\,Mpc^{-1}} \), the model reproduces both the local supernova observations and the CMB-inferred expansion rate, thereby resolving the long-standing Hubble tension. The reversible UBH cosmology thus provides a physically coherent synthesis linking fractal entropy growth, scale-dependent curvature, and information conservation. Future work will focus on the inclusion of BAO and gravitational-wave constraints to further test this emerging picture of a self-similar, entropy-conserving Universe.