Universal Memory and the Law of Fractal Consistency

We present a journal-ready large-scale-structure manuscript on Universal Memory within the Law of Fractal Consistency (FCL/LCF). The aim is deliberately restricted. We do not claim that the current analysis replaces ΛCDM as a fully closed cosmology, nor that DESI DR1 by itself proves the microscopic ontology of the broader FCL program. Instead, we test whether the luminous red galaxy sample in DESI Data Release 1 exhibits a reproducible large-scale summary signature compatible with an asymptotic consistency attractor and an unusually low-dispersion sector under repeated pipeline perturbation. The dataset is split into North and South Galactic Cap regions and three redshift bins, and the extraction pipeline is rerun under 30 independent stochastic seeds, yielding 180 estimates of the triplet (p1, p2, rH). The main empirical result is that the large-scale summary p2 clusters near 7.3953 with a standard deviation of 0.0253, substantially tighter than p1, with standard deviation 0.0618, and vastly more stable than rH. The attractor value phi0 = ln(6π5) = 7.5154 is not exactly reached; the global gap remains ΔA = 0.1201. That non-saturation is scientifically preferable to artificial exact agreement and supports the safer language of attractor-oriented convergence rather than completed convergence. We further formalize a covariance-aware statistical layer, a vector-based hemispheric contrast test (QH = 1.44, p = 0.696), and a hostile null/mock program based on geometry-matched ΛCDM mocks, shuffled-data baselines, and estimator perturbation families. The paper is therefore strongest when read as a falsifiable, covariance-conscious observational study of repeatability and rigidity in the cosmic web, not as a closure claim on fundamental cosmology.