Universal Rotation of Cosmic Filaments: A Fractal Cascade Derivation

Multiple independent surveys have detected systematic tangential galaxy velocities around cosmic filament axes — a universal rotation signal of 𝑣rot ≈ 110 km/s, independent of filament mass, length, or redshift. Standard ΛCDM structure formation predicts negligible net rotation from irrotational initial conditions, making this one of the unexpected large-scale structural features of the universe. We propose a derivation within the Fractal Mechanics (FM) framework: filament rotation velocity is 𝑣rot ≈ 𝐻0 × 𝑅cross, where 𝑅cross is the characteristic cross-sectional radius and 𝐻0 is the Hubble parameter. For 𝑅cross ≈ 1.6 Mpc (set by the baryon acoustic scale at filament formation): 𝑣rot ≈ 70 × 1.6 = 112 km/s, consistent with observations. The universality of 𝑣rot follows from 𝐻0 being approximately constant across the redshift range probed (𝑧 < 0.5). The FM cascade interpretation: new quantum nodes emerge at rate 𝑛 = 𝐻(𝑡)/ ln 𝜑 as the universe expands; their tangential velocity at scale 𝑅cross is 𝐻 × 𝑅cross, manifesting as filament rotation. Using our previously published Hubble tension resolution 𝐻0 (𝑧) = 𝐻0_base √[1 + 𝛼/(1 + 𝑧)³], we predict 𝑣rot decreases by < 2% from 𝑧 = 0 to 𝑧 = 1 — testable with Euclid and DESI spectroscopic surveys. A connection between filament rotation and the observed dark energy density is derived.