A Late-Time Geometric Suppression of Structure Growth Beyond ΛCDM

We investigate an effective late-time cosmological extension, the J-core, as a geometrically motivated mechanism for mildly suppressing the growth of large-scale structure while preserving an approximately standard background expansion history. The model is designed to capture, at the phenomenological level, the type of late-time structural consistency effects expected in the broader framework of the Fractal Consistency Law (FCL), without yet requiring a fully microfounded Boltzmann-level derivation. Its observational role is therefore to test whether a controlled late-time suppression sector can improve the joint fit to current expansion and growth data. We confront the effective J-core with a combined late-time pipeline including Pantheon+SH0ES supernovae, DESI DR2 BAO, and public fσ8 measurements, using a ΛCDM baseline and a direct MCMC comparison under the same general framework. In the primary completed chain, the J-core improves the best-fit likelihood relative to ΛCDM by Δχ² = −9.59 with ΔAIC = −3.59 and ΔBIC = +12.75. Thus, the model achieves a statistically nontrivial gain in fit quality and survives the Akaike penalty for additional parameters, although it does not yet defeat the minimal baseline under the stronger Bayesian Information Criterion. The preferred suppression amplitude is positive, Aj = 0.0188 ± 0.0082, corresponding to an indication at roughly the 2.3σ level for a nonzero late-time growth-suppression effect. A second rerun with substantially healthier sampler behavior confirmed that the central posterior region remains stable when the acceptance rate is brought into a much more credible regime. Although that rerun was interrupted by cloud-runtime loss before the final posterior tails were fully archived, it reached very strong convergence of posterior means, reinforcing the conclusion that the J-core signal is not an obvious artifact of pathological proposal dynamics. The combined evidence therefore supports a cautious but important claim: the effective J-core is no longer observationally inert and has become a genuinely competitive late-time extension, even though a persistence-safe final rerun and a tighter microscopic derivation are still required before it can be presented as a mature alternative to ΛCDM across the full precision-cosmology landscape.