Large-Scale Cosmic Structures as Fibonacci Cascade Solitons: The Big Ring, Giant Arc, and the Hierarchy of Anomalous Structures

Six anomalously large cosmological structures — the Big Ring (1. 3 Gly), the Clowes-Campusano LQG (~1. 6 Gly), the Giant Arc (3. 3 Gly), the Huge-LQG (4. 0 Gly), the GRB Ring (5. 6 Gly), and the Hercules-Corona Borealis Great Wall (~10 Gly) — challenge the cosmological principle by exceeding the ΛCDM homogeneity scale by factors of 3–8. We propose that all six structures are Fibonacci cascade solitons within the Fractal Mechanics (FM) framework, occupying cascade levels n = 287–291 where nₘax = 291 corresponds to the current Hubble radius. Their sizes follow a 𝜑ᵏ ladder (𝜑 = 1. 618), with the Hercules-Corona Borealis structure at n = 291 representing the maximum stable soliton in the present-epoch cascade. The co-location of the Big Ring and Giant Arc at z ≈ 0. 80 is explained by triadic cascade coupling at levels (n, n-1, n-2) = (289, 288, 287), predicting an intermediate structure at ∼ 2. 0 Gly at the same redshift. The cardioid geometry of the FM Big Bang predicts: (i) a preferred cosmological axis aligned with the CMB hemispherical asymmetry; (ii) large-scale galaxy spin chirality; and (iii) coherent filament rotation — independently observed at 5. 4 sigma (Böhme et al. 2026), in JWST deep fields (Shamir 2025), and in individual filaments (Wang et al. 2021; Tudorache et al. 2025). FM provides a unified explanation requiring no new physics beyond the cascade structure derived in Leroy & Claude (2026a).