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In this letter, we demonstrate a novel approach to calculating the integral density of the Observable Universe within the framework of a material, viscous rheological substrate model (the OCEAN paradigm). By abandoning abstract cosmological corrections such as Dark Matter and Dark Energy, and analyzing the strict physical volumes and spatial distribution of the main morphological types of galaxies (2 × 10^12 structures), we find that the average baryon density of the Universe explicitly converges to the fundamental geometric constant π × 10^−27 kg/m3. When accounting for three-dimensional isotropic expansion, the dynamic effective density reaches a precise mirror equilibrium with the calm vacuum substrate invariant (ρ_eff = 9.22×10^−27 kg/m^3). This numerical resonance provides strong evidence that π is not merely an abstract mathematical ratio, but a fundamental quantum-mechanical boundary of spatial packing in a fluidic Universe.
Shlyapik A. 2026. The Geometric Invariant of Meta-Galactic Density: A Path to the Physical Nature of π. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115688
