Cosmology of the Creating Vacuum: Brane Formalism and UV/IR Geometric Inversion at the Submillimeter Scale

This paper presents the rigorous mathematical and geometric formalization of the extended cosmological model "Cosmology of the Creating Vacuum". The model is integrated into the Einstein-Hilbert action formalism applied to a fluid 3-brane embedded in a five-dimensional (5D) quasi-de Sitter Bulk. By decoupling the brane tension from the rigid Planck scale and calibrating it to the energy scale of neutrinos / late quantum vacuum, λ ≈ (2.3 meV)⁴, the model provides a natural geometric resolution for the Hubble Tension, demonstrating that the 5σ discrepancy represents a local density effect within the Laniakea galactic supercluster. In addition, the paper formalizes the principle of UV/IR geometric inversion at the critical scale R₀ = 85 μm. It is analytically demonstrated that the null results of torsion experiments below this threshold do not invalidate the model, but rather confirm the predictable collapse of the macro-gravitational potential into the potential well of the quantum confinement regime. The model provides strict predictive maps for the Chevallier-Polarski-Linder (CPL) parameters, making it fully falsifiable.