Hydrodynamic Foundations of the Three-Rank Fractal Architecture: A Real Compressible Fluid Medium as a Unified Physical Origin for Perihelion Precession and Cosmological Redshift

AbstractThis paper proposes hydrodynamic foundations for the Three-Rank Fractal Architecture,modeling the Universe not as a geometric abstraction of curved spacetime, but as a realcompressible viscoelastic fluid medium structured into three nested ranks: the G-medium (Rank0), the Electromagnetic (EM) medium (Rank 1), and discrete atomic matter (Rank 2). Thecompressibility and viscoelastic properties of the fluid provide the physical foundation for thelarge-scale interaction between macro-rotors and wave solitons.First, the anomalous perihelion precession of Mercury is derived as a mechanical phase lagdriven by a non-linear pressure gradient (\nabla P \propto 1/r^4) caused by the localcompression and density variation of the EM medium surrounding the solar macro-rotor.Utilizing the empirical refractive index profile n(r) from Cassini radio-science data, a precisematch of 42.98'' per century is analytically established. It is mathematically demonstrated thatthe 1/r^4 force gradient corresponds directly to the spatial derivative (force projection) of the1/r^3 potential term in General Relativity.Second, cosmological redshift is interpreted as a coherent viscoelastic attenuation ofelectromagnetic solitons propagating through the compressible G-medium. The introduction of athreshold distance explains the absence of the effect on local scales due to masking bynon-linear fluctuations, transitioning via statistical averaging into a strictly linear macro-regime(Hubble's law) while fully preserving time dilation and image coherence. The presented fluiddynamic framework successfully unifies wave optics and celestial mechanics into a singlecausal reality.Keywords: Hydrodynamic foundations, Compressible fluid, Three-Rank Fractal Architecture,EM medium, Perihelion precession, Mercury, Cassini data, Pressure gradient, Tired light,Cosmological redshift, Threshold distance, Stationary Universe.