Global Saturation, Cosmic Expansion, and Effective Vacuum Energy in the TUO Framework.

Article V : Observationally Anchored Consistency of Global Saturation at Cosmological Scale as a Test of the Maillot Invariant This article provides a minimal, observationally anchored consistency test of the TUO global saturation framework at cosmological scale. Treating the Hubble horizon as an effective global cavity and using only standard kinematic identifications, we show that the observable universe lies at the saturation fixed point predicted by the Maillot invariant once physical realizability conditions—namely isotropy and phase closure—are imposed. The result is not a parameter fit and does not rely on modified Friedmann dynamics, additional fields, or model-dependent assumptions. It establishes the observable universe as a regulated system maintaining global saturation under expansion. The constitutive energetic interpretation of this saturation condition is developed independently in Article VI. ------- Article VI : Effective Vacuum Energy Density from Global Saturation in the TUO Framework The standard quantum-field-theoretic estimate of vacuum energy diverges because it lacks a global physical constraint associated with physical realizability. Within the TUO framework, physical realizability imposes a universal saturation condition enforced by vacuum tension. This article derives an effective vacuum energy density as a secondary, emergent quantity constrained by global saturation rather than postulated as a fundamental divergent object. The ultraviolet bound arises naturally as a stability limit dictated by saturation, eliminating arbitrariness and resolving the vacuum energy problem without introducing new fields or parameters. This work provides the constitutive energetic counterpart to the cosmological consistency test established in Article V.