Part 4: The Entanglium Aether Equations – Full Mathematical Derivation of the 5D → 4D Fractal Aether, the SNN Constant from E8 Symmetry, and Integration with CERN Heavy-Ion Physics

This paper (Part 4 of the Fractal-Unified Field Theory series) presents the complete mathematical derivation of the Entanglium Aether Equations: the 5D to 4D reduction of the fractal vacuum. The Lorenz-gauge electromagnetic vacuum emerges from a compactified 5th dimension with fractal measure, yielding a universal fractal dimension D_SNN = 1.830 ± 0.008 derived from E8 root lattice projections into 4D. The dimension matches empirical data across:• Solar-wind turbulence• Gamma-ray burst engines• Quark–gluon plasma multifractality (ALICE 2023–2025)• Cosmic web structure• Magnetic free-energy scaling Full derivations include the 5D action reduction, fractal measure emergence, SNN constant origin, and integration with CERN heavy-ion collision data. Supplementary: Detailed equations, E8 projections, path integrals, and CERN data fits (remaining pages).