Fractal–classical transition of space-time : IFS, DSI, and Hausdorff sigmoid to FLRW (Part Two, statistical comparison with observational data)

This study follows on from Fractal–classical transition of space-time : IFS, DSI, and Hausdorff sigmoid to FLRW, which introduces an effective geometric framework (IFS/DSI) describing a transition driven by an effective Hausdorff dimension HD. In this framework, it is shown that an inflationary phase can be reproduced at the effective level, without resorting to an explicit inflaton field, under the assumption of a rapid transition from HD in the ultra-early times.The present study extends the analysis to low redshifts and examines late acceleration using two tests. The first test reconstructs E(z)=H(z)/H0 from type Ia supernovae (Pantheon+SH0ES, DES-SN5YR) and cosmic clocks, taking into account covariances. It highlights a bimodality of solutions for H0, strongly influenced by a point with high leverage around z≃1.037, which underscores the sensitivity of absolute anchoring to the data structure. The second test explores a regular parameterization of HD(z) (sigmoid tending towards a plateau of the order of HD∼6), possibly supplemented by a late modulation of low amplitude. The results indicate that SN Ia mainly constrain a smooth evolution of E(z), compatible with a moderate late acceleration centered around z∼0.6−0.8, without requiring highly non-standard dynamics. The study concludes that this framework remains compatible with the data considered, while emphasizing that independent constraints (notably anisotropic BAO) will be decisive in resolving degenerations and testing the falsifiability of the geometric interpretation.