The Fractal Hierarchy of the Universe as a Predictive Instrument: Extrapolating Unobserved Large-Scale Structure from Known Scaling Laws

The large-scale structure of the observable universe exhibits a well-documented fractal hierarchy: the Local Group, Laniakea, and the Shapley Attractor are related by consistent power-law scaling relations. We propose that these measured scaling relations can be used as a predictive instrument: if fractal self-similarity holds beyond the current observational horizon, the properties of the next unobserved level of the hierarchy can be derived from the known levels below it. We compute specific, falsifiable predictions for the mass, distance, and directional influence of a hypothetical super-attractor beyond Shapley, and identify observational signatures testable with Euclid, CosmicFlows-5, and existing DESI DR1 data. This paper stands independently but is motivated in part by the fractal convergence hypothesis presented in Beyer (2026c,zenodo.org/records/20037413).